But How Do It Know: The Basic Principles of Computers for Everyone

But How Do It Know The Basic Principles of Computers for Everyone J Clark Scott BUT HOW DO IT KNOW The Basic Principles of Computers For Everyone By J Clark Scott a b c Copyright 2009 by John Clark Scott Computer design incorporated herein Copyright 2009 by John Clark Scott All Rights Reserved Published by John C Scott Oldsmar FL 34677 ISBN 9780615303765 buthowdoitknowcom Cover art photography and design by Alexander C Scott III artbyalexscottcom Printed in the United States of America First Edition July 2009 10 9 8 7 6 5 4 3 2 1 INTRODUCTION The title of this book is the punch line of an old joke that goes like this Joe is a very nice fellow but has always been a little slow He goes into a store where a salesman is standing on a soapbox in front of a group of people The salesman is pitching the miracle new invention the Thermos bottle He is saying It keeps hot food hot and cold food cold Joe thinks about this a minute amazed by this new invention that is able to make a decision about which of two different things it is supposed to do depending on what kind of food you put in it He cant contain his curiosity he is jumping up and down waving his arm in the air saying but but but but Finally he blurts out his burning question But how do it know You may or may not have laughed at the joke but the point is that Joe looked at what this Thermos bottle could do and decided that it must be capable of sensing something about its contents and then performing a heating or cooling operation accordingly He thought it must contain a heater and a refrigerator He had no idea of the much simpler principle on which it actually operates which is that heat always attempts to move from a hotter area to a cooler area and all the Thermos does is to slow down this movement With cold contents the outside heat is slowed on its way in and with hot contents the heat is slowed on its way out The bottle doesnt have to know in order to fulfill its mission and doesnt heat or cool anything And eventually the contents hot or cold do end up at room temperature But Joes concept of how the bottle worked was far more complicated than the truth So the reason for the book title is that when it comes to computers people look at them see what they can do and imagine all sorts of things that must be in these machines Or they imagine all sorts of principles that they must be based on and therefore what they may be capable of People may assign human qualities to the machine And more than a few find themselves in situations where they feel that they are embarrassing themselves like our friend in the joke Joe But computers are actually quite easy to understand Of course computers have a greater number of parts than a Thermos bottle but each part is extremely simple and they all operate on a very simple very easy to understand principle With the Thermos the principle is that of the motion of heat This is something we can observe in life We see ice cubes melting when they are removed from the freezer and we see the hot meal cooling off on the table when the family is late for dinner In the computer the principle on which it operates has to do with electricity but that doesnt mean that it is hard to understand If you have observed the fact that when you turn on a light switch a light bulb lights up and when you turn the switch off the light goes dark then you have observed the principle on which computers operate That is about all you need to know about electricity to understand computers JUST THE FACTS MAAM This book is not primarily intended to be a textbook There are no problems to do at the end of each chapter Its intention is simply to demystify the subject of computers for anyone who has ever wondered whats going on inside of that box Of course it also makes a perfect introduction to computers for a young person who will ultimately go on to get a PhD in Computer Science But it should be easily understandable by housewives senior citizens and children who can read well It should be understandable to plumbers and street sweepers It requires no previous technical education It only requires that you can read the language you can turn a light bulb on and off and you can do very simple addition on the order of 8513 This book presents the complete essentials that make up a computer It presents every piece and part in the proper order so that each one will make sense and can be understood Every part is explained fully and every new word is defined thoroughly when it is first used Any attempt to simplify the subject further would leave gaps in the big picture where someone would still have to guess how the parts work together and you just wouldnt ever have that Aha I get it moment that I think youll soon have This book is not a dumbeddown version of some college textbook It is a complete explanation of the basic principles of computers It is a technical book but so is a cookbook and so is a drivers education handbook This book just starts at the beginning and defines every item needed to understand the machine No matter what someone already knows about computers this will fill in any missing pieces and put them all together into something that makes sense Even our friend Joe could understand this book with diligent study There are thousands of words and ideas associated with the field of computers that make the whole subject seem like a mess But the basic concepts underlying them are simple In this book there will not be volumes of trivia about the construction or history of computers just the essentials no more and no less Each part of the computer has a simple function and when they are connected together you end up with a useful machine called a computer There is nothing to memorize in this book Each chapter is designed to give you a new idea that you didnt have before or if it is something that you had heard about previously it always seemed confusing Each idea is very simple and one thing leads to the next Each chapter presents an idea Each idea is simple and easy to understand Later chapters present ideas that build on the ideas from previous chapters If someone were to write a book about how to build a house there could be various levels of detail The simplest book would say lay a foundation put up the walls cover with a roof put in plumbing and electrical and youre done That would not be enough detail for someone who didnt already have some experience using a hammer and saw and installing a faucet and wiring a light switch At the other end of the spectrum would be a book that had separate chapters for every possible type of foundation the different kinds of dirt you might have to dig in formulas for a dozen different kinds concrete charts of weather conditions that are optimum for laying foundations etc That would be far too much information There would be so many details that what was really important would get lost This book attempts to give just enough detail to see what every computer has in common and how they work not how to build the biggest or best computer ever made It is not about any specific brand of computer It is not about how to use a computer If it were a book about building a house it would probably describe a simple plan for a sturdy garden shed with a sink and one bare light bulb showing the size and shape of every piece of wood where to put all the nails how to hang the door and how to put the water pipes together so they wouldnt leak It would not show how to build anything as complicated as a fancy curved oak staircase We are going to show the one simple part that computers are made of and then connect a bunch of them together until we have built a complete computer It is going to be a lot simpler than you ever imagined SPEED Computers seem mysterious and magical How can they do what they do They play games they draw pictures they know your credit rating These machines are capable of doing all sorts of strange and wondrous things Yet they are simple They can do only a very few very simple things And they can only do one of these simple things at a time They appear to be doing complex things only because they do a huge number of simple things one after another in a small amount of time The result as in a video game is very complex in appearance but in reality is very simple just very very fast Computers are designed to do a small number of specific simple things and to do these things quickly one after the other Which simple things are done and in what order determines what sort of task the computer accomplishes in any given time but anything the computer does consists of nothing outside of its limited capabilities Once you see what a computer is made up of you will come to realize how it is that they can do what they do exactly what sorts of things they are capable of and also what they are not capable of So the secret of computers is not that they are complex rather it is their speed Lets look at exactly how fast their speed is Since computers work on electricity their speed is related to the speed of electricity You may remember hearing that the speed of light is 186000 miles per second Thats pretty darned fast Light can go around the entire earth seven times in one second or from the Earth to the Moon in about a second and a half Per the physicists electricity has many properties in common with light and its speed when traveling in a wire gets slowed down to about half the speed of light But still going all the way around the Earth three and a half times in one second is extremely fast As a point of comparison imagine it is a hot day and you have an electric fan sitting on the table blowing cool air on you The fan is spinning around so fast that the blades are a blur but it is only spinning around about 40 times each second A point on the edge of one of those blades will only travel about 150 feet in that second it will take 35 seconds for that point to travel just one mile Since the fan blades are already a blur it may be hard to imagine them going just ten times faster If it did that fan would be putting out quite a breeze And if you could make it go a hundred times faster it would almost certainly selfdestruct with fan blades breaking off and getting stuck in the ceiling But electricity traveling in the same circle would go around about a hundred million times in one second thats two and a half million times faster than the fan blades Thats fast A million is a very large number If you took a big sheet of paper that was 40 inches square and took a ruler and placed it at the top edge and drew 25 dots per inch along the top edge of the paper you would have to draw one thousand dots to get across that sheet of paper If you then moved the ruler down the page 125 of an inch and drew another thousand dots and kept doing that you would have to move the ruler down the page one thousand times each time drawing one thousand dots If you could complete such a boring task you would end up with a piece of paper with a million dots on it Thats a lot of dots or a lot of anything And just to finish the thought if you could find a thousand people who would each draw one of these million dot sheets and stacked up those thousand sheets in a pile you would then have a billion dots Now lets say that the electricity moving around inside the computer can accomplish some simple task by traveling one foot That means that the computer could do 500 million simple things in one second Again for comparison the fan on the table will spin for 7 hours to go around just one million times and it will take a full six months for it to spin around 500 million times When you talk about the speed that electricity can move between parts inside the computer some of the parts you can see are a foot apart some are closer an inch a tenth of an inch And inside these parts are a multitude more parts that are very close to each other some just thousandths of an inch apart And the shorter the distance the electricity has to travel the sooner it gets there There is no point in saying how many things todays computers do in a single second because that would date this book Computer manufacturers th continue to produce new computers that go twice as fast as the fastest computers of only two or three years past There is a theoretical limit to how fast they can go but engineers keep finding practical ways to get around the theories and make machines that go faster and faster During all of this time that computers have been getting faster smaller and cheaper the things that computers do really have not changed since they were first invented in the 1940s They still do the same few simple things just faster cheaper more reliably and in a smaller package There are only a few sections to a computer and they are all made out of the same kinds of parts Each section has a specific mission and the combination of these parts into a machine was a truly marvelous invention But it is not difficult to understand LANGUAGE In this book we are going to need to define some words that are used to describe the parts inside a computer In some professions notably the Medical and Legal there is a tendency to make up a lot of new words and to take them from the ancient Greek and Latin languages and to make them long and hard to pronounce In the world of computers it seems that the pioneer inventors were a less formal sort of people Most of the words they used are simple words from everyday language words that already existed but are used in a new way Some of the new words are words we already know used as a different part of speech like an existing noun now used as a verb Some of the words are acronyms the first letters from the words of a phrase Each word will be described thoroughly when it is first used And although there are thousands of words and acronyms in use if you consider the entire computer industry there are only about a dozen or two words needed to understand the computer itself You have probably heard some of these words before and figured out what they meant from how they were used but now you will get the proper and full definitions In many cases you may find that they are simpler than you thought JUST A LITTLE BIT What is in a computer It shows you still pictures moving pictures music your checkbook letters you have written it plays video games communicates all around the world and much much more But are there pictures inside the computer If you got out a microscope and knew where to look could you find little pictures somewhere inside the computer Would you see As and Bs and 8s and 12s moving around in there somewhere The answer is no there are no pictures numbers or letters in a computer There is only one kind of thing in a computer There are a large number of this kind of thing but there is only one kind of thing in there It is called a bit When you flip a coin up in the air and let it fall on the ground it will end up on the floor in one of two possible states with either the head showing or the tail The light in your living room assuming you have a switch and not a dimmer can be either on or off The lock on your front door can be either locked or unlocked What do all of these things have in common They are all places that contain a thing that can be in one of two possible states This is the definition of a bit A bit is some kind of a physical object that has a size and a location in space and it has some quality about itself that at any given time can be in one of two possible states and maybe made to change back and forth between those two states A lump of clay is not a bit It can be molded into a ball a cube a pancake a ring a log a face or anything else you can think of It has a size and a location in space but there are too many states that it can be in for it to be called a bit If you took that lump of clay flattened it out scratched yes on one side of it and no on the other side and then put it in a kiln and fired it until it was hard then you might be able to call it a bit It could sit on a table with either the yes or no showing Then it would only have two states You have probably heard of bits before in relation to computers and now you know what they are In a computer the bits are not like the coin or the lock they are most like the light That is the bits in a computer are places that either have electricity or they do not In a computer the bits are very very small and there are a very large number of bits but thats all that is in there Like the light in the living room the bit is either on or off In the living room there is electricity in the wall coming into the switch When you turn the switch on the electricity goes from the switch through the wires in the wall and ceiling into the light socket and then into the light bulb So this bit in the living room is several feet long it includes the switch the wires the socket and the light bulb In a computer bits are mostly tiny actually microscopic Also the computer bit doesnt have a mechanical switch at one end or a light bulb at the other If you removed the light bulb from the socket in the living room the switch would still send electricity to the socket when it was on and it would still be a bit you just wouldnt be able to see whether it was on or off by looking at a light bulb Your computer has something resembling switches like the keys on the keyboard and something resembling light bulbs like the tiny dots on the screen but most of the bits are inside and unseen This is basically all there is in a computer bits There are lots and lots of them and they are arranged and connected up in various ways which we will examine in detail as the book progresses but this is what is inside all computers bits A bit is always in one of its two possible states either off or on and they change between on and off when they are told to do so Computer bits arent like the coin that has to physically flip over to change from one state to the other Bits dont change shape or location they dont look any different they dont move or rotate or get bigger or smaller A computer bit is just a place if there is no electricity in that place then the bit is off When electricity is present then the bit is on If you want to change a coin from showing heads to showing tails you have to physically move it to flip it over which takes some amount of time Because the only thing that has to move in a computer bit is the electricity changing its state from off to on or on to off can happen much more quickly than anything that has to be moved physically As another example remember the wild American west from the movies There were little towns separated by vast distances The bigger towns would have a telegraph office In this office was a guy wearing a funny hat who had a springloaded switch called a key and he would send messages by pressing this key on and off in certain patterns that represented the letters of the alphabet That key was connected to a battery yes they had batteries back then and a wire that was strung along poles until it got to another town The key simply connected the battery to the wire when it was pressed and disconnected the battery when the key was not pressed In the other town there was another telegraph office the wire came into that office the end of it was wrapped around an iron rod which turns into a magnet when there is electricity in the wire the magnetized rod attracted a little bar of iron held nearby with a spring and made a clicking sound every time the electricity came on The guy in the office listened to the pattern of the clicking and wrote down the letters of the message They might have used a light bulb instead of the clicker except that light bulbs had not yet been invented The point of bringing up this subject is that this whole telegraph machine from the key that gets pressed in one town through the long wire that travels to another town many miles away to the clicker this whole apparatus comprises just one single bit It is a place that can either have or not have electricity and goes on and off as it is told And this method of communication revolutionized the world in many ways But this very important invention of the 1840s consisted of nothing more than one bit So I hope this begins to simplify the subject of computers for you There is only one thing inside computers bits Lots of them to be sure but when you understand bits you understand whats in there WHAT THE Imagine it is a bright sunny day and you walk into a room with lots of open windows You notice that the ceiling light is on You decide that this is a waste and you are going to turn the light off You look at the wall next to the door and see a switch plate with two switches So you assume that the one closer to the door is for the ceiling light But then you notice that the switch is already off And the other switch is off too So then you think well maybe someone installed the switch upside down so you decide to flip the switch anyway You flip it on and off but nothing happens the ceiling light stays lit So then you decide that it must be the other switch and you flip it on off on off Again nothing happens that ceiling light continues to shine at you You look around there is no other door there are no other switches no apparent way to turn off this darned light It just has to be one of these two switches who built this crazy house anyway So you grab one switch with each hand and start flipping them wildly Then suddenly you notice the ceiling light flicker off briefly So you slow down your switch flipping and stop when the ceiling light is off Both switches say on and the light is now off You turn one switch off then on and the light goes on then back off This is backwards One switch off equals light on So then you turn the other switch off then on the same thing the light goes on then back off What the heck Anyway you finally figure out how it works If both switches are on the light goes off If one or the other or both switches are off then the ceiling light is on Kind of goofy but you accomplish what you intended you turn both switches on the light goes off and you get the heck out of this crazy room Now what is the purpose of this little story about the odd light switches The answer is that in this chapter we are going to present the most basic part that computers are made of This part works exactly like the lighting system in that strange room This computer part is a simple device that has three connections where there may or may not be some electricity Two of those connections are places where electricity may be put into the device and the third connection is a place where electricity may come out of the device Of the three connections two of them are called inputs because electricity can be sent to them from somewhere else The third connection is called the output because electricity can come out of it and then be sent somewhere else This computer part is a device that does something with bits If you have two bits and you connect those two bits to the inputs this device looks at those two bits and decides whether to turn the one output bit on or off The way it decides is very simple and is always the same If both inputs are on the output will be off If one or both of the inputs are off then the output will be on Thats just the way that the room with the odd light switches worked Remember that there is nothing but bits inside the computer This simple device is where bits come from and where they go to The decision that this device makes is how bits come to be turned on and off in a computer Two bits go into the device and one bit comes out Two bits come from somewhere else are examined by the device and a new third bit is generated so that it may go somewhere else If you have been extra observant you may have asked yourself this question when both inputs are off the output is on so how do you get electricity at the output if both inputs are off Well that is an excellent question and the excellent answer is that every one of these devices is also connected to power Like every appliance or table lamp in your house where each has a plug with two pins this device has a pair of wires one of which is connected to a place where the electricity is always on and the other is connected to a place where the electricity is always off This is where the electricity for the output comes from When someone builds a computer they have to make all of those power connections to each one of those parts in order to have it work but when we are drawing diagrams of parts how they are connected and what they will do we wont bother drawing the power wires they would just clutter up the drawing It is understood that each part has its power connection and we dont worry about it Just understand that it is there and we wont mention it any more for the rest of the book I wouldnt have even mentioned it here except that I figured that youd probably ask yourself that question sooner or later Now I know I said that you dont have to understand much about electricity to understand computers Here is as complicated as it gets There are actually a half dozen electronic parts inside of this device that make it work but we are not going to examine those parts in this book Someone who has an electronics background could look at whats in there and in about 30 seconds would say Oh yeah if both inputs are on the output will be off and for any other combination the output will be on just like the book says And then that person could go ahead and read this book without ever having to think about whats in there again Someone who doesnt know electronics misses out on those few seconds of understanding but this book is the same for everyone In normal house wiring one switch turns one light on and off In the computer it takes two switches and its sort of backwards in that they both have to be on to turn the light off But if you accept the fact that something could be made that operates this way you can then understand how everything in the computer works This type of computer part is in fact the ONLY type of part required to build a computer Of course it takes a lot of them to build a complete computer but with enough of them you can make any type of computer So there you go again see how simple a computer is It is just full of this little type of thing a lot of them to be sure but this is all there is Now we need to give this device a name this thing inside the computer that bits are made of it is called a gate I cant find a good reason why it is called a gate a gate in a fence lets people through when it is open and stops people when it is closed A computer gate generates a third bit from two other bits it doesnt open and close or stop or let anything through The meaning of this computer term gate doesnt seem to fit into the common meaning of the word but sorry I didnt make up the name thats just what it is called Youll get used to it At least it isnt some long word from the ancient Greek In the next few chapters we are going to show how we can do something useful by connecting several gates together We will use drawings like the following The D shape with the little circle at its tip represents the device we have described and the lines represent the wires going in and coming out of it that get attached to other parts of the computer The picture on the left shows a gate complete with its power wires but as promised we wont be concerned with them for the rest of this book The drawing on the right shows everything we need This is a representation of a gate The two wires on the left a and b are the inputs and the wire on the right c is the output All three wires are bits which means that they are either on or off Each input bit comes from somewhere else in the computer and is either on or off depending on what is happening where it came from and then this gate sets its output on or off depending on the states of its two inputs Sometimes it is useful to make a little chart that shows how the various input combinations create the output like this Each line shows one possible combination of the inputs and what the output will be under those circumstances Compare this little chart with the experience with the odd room with the two light switches If one switch is called a the other switch is called b and the ceiling light is called c then this little chart describes completely and exactly how the equipment in that room operates The only way to get that light off is to have both switch a and switch b on SIMPLE VARIATIONS As mentioned this gate is the only thing you need to build a computer but you need a lot of them and they have to be wired together in an intelligent manner in order to be able to make them do something useful What we are going to do here is to show two simple things that are done many times inside any computer This first one is very simple Take the gate above and take the two input wires a and b and tie them together Thus a and b will always be the same They can still be changed on and off but a and b can never be different A and b can either both be on or both be off Thus the chart of this combination only has two lines on it two possibilities Actually since columns a and b are the same there is really only one input and it can be drawn simply like this with a triangle instead of the D shape Its chart is also very simple For our second variation lets combine one of our original type of gate with the new gate that we just invented like this And well combine the charts of how they work The a b and x are like the first gate the x and c are like the second gate This combination is used so often inside computers that it is built as a single unit and the x bit is not available to connect to So to make it simpler to understand it is drawn as a single unit like this The only difference between this picture and the picture of our original gate is that the little circle after the big D is missing Since x is not used the chart can also be simplified and it looks like this The only difference between this chart and the chart of our original gate is that every item in column c is the opposite of what it was in the original chart Imagine that this combination of gates was installed in that room with the two light switches and the ceiling light The only way the light could be on is if both switches were on So if you walked in there and saw the light on and then looked at the switches you would see that they were both on No matter which switch you decided was for the light and you switched it off the light would go off You might not notice that if you turned both off and then wanted to turn the light back on you wouldnt be able to do it by just flipping one switch You would have to go through the same experiment flipping both switches until the light came on and you would find that one switch and the other switch would have to be on to get the light to light This combination gate could be described this way For the output to be on one input AND the other input must both be on Thus this type of gate has a name and in the tradition of the informal terminology invented by computer people because it reminds us of what the word AND means it is simply called an AND gate Now to fill in a few details purposely left out above the original gate we looked at works like the AND gate except the output is the opposite or the negative of the AND gate Thus it is called a Negative AND gate or just a NAND gate for short The simple gate that had both inputs tied together also has its own name The output is always the opposite of the one input that is if the input is on the output is not on off If the input is off the output is not off on The output is always NOT what the input is thus it is called a NOT gate Notice the difference between the diagrams of the AND gate and the NAND gate They are the same except that there is a little circle at the beginning of the output of the NAND gate The thing that looks like a large letter D means to do the AND function which means to take action only if both inputs are on and the little circle means switch to the opposite So an AND gate is on if both inputs are on a NAND gate is off if both inputs are on The NOT gate starts with a triangle which just means take the input and turn it into an output The circle then means to switch to the opposite The AND gate is used a lot in computers and it is probably the easiest to understand but we looked at the NAND gate first for two reasons The first and less important reason is that the NAND gate is the easiest gate to build When you have to build a large number of gates it will be cheaper and more reliable if you can use the type of gate that is easiest to build The second and very important reason that we looked at the NAND gate first is this That everything in a computer that makes it a computer can be made out of one or more NAND gates We have already seen that the NOT gate and the AND gate can be made out of NAND gates and we will see a few more interesting combinations as we go along But every one of them is based on this silly little thing called a NAND gate The problem in this chapter has been that the NAND gate is the basic building block of computers but the AND gate is the first gate that has a name that makes sense So we looked first at the NAND gate and the NOT gate without giving them names Then we built an AND gate gave it its name and went back and named the first two As a note on the language here the word and is a conjunction in regular English It connects two things as in I like peas and carrots In computers we use the word in two new ways First it is an adjective a word that modifies a noun When we say this is an AND gate the word gate is a noun and the word AND tells us what kind of a gate it is This is how AND has been used in this chapter AND will also be used as a verb as in let us AND these two bits We will see AND used in this way later in the book So back to the simplicity theme of this book we have said that there is only one thing in computers bits And now we see that bits are constructed using gates and all gates come down to the NAND gate So all you have to know to understand computers is this very simple device the NAND gate No kidding Can you understand this thing Then you can understand the whole computer DIAGRAMS If you want to see how a mechanical machine works the best way to do it is to look inside of it watch the parts move as it operates disassemble it etc The second best way is to study it from a book that has a lot of pictures showing the parts and how they interact A computer is also a machine but the only thing that moves inside of it is the invisible and silent electricity It is very boring to watch the inside of a computer it doesnt look like anything is happening at all The actual construction of the individual parts of a computer is a very interesting subject but we are not going to cover it any further than to say the following The technique starts with a thin crystal wafer and in a series of steps it is subjected to various chemicals photographic processes heat and vaporized metal The result is something called a chip which has millions of electronic parts constructed on its surface The process includes connecting the parts into gates and connecting the gates into complete computer sections The chip is then encased in a piece of plastic that has pins coming out of it Several of these are plugged into a board and there you have a computer The computer we are going to build in this book could easily fit on one chip less than a quarter of an inch square But the point is that unlike a mechanical machine the actual structure of a chip is very cluttered and hard to follow and you cant see the electricity anyway The diagrams we saw in the previous chapter are the best way to show how a computer works so wed better get pretty good at reading them Throughout the rest of this book we are going to build new parts by connecting several gates together We will describe what the new part does and then give it a name and its own symbol Then we may connect several of those new parts into something else that also gets a name and a symbol Before you know it we will have assembled a complete computer Every time there is a new diagram the text will explain what its purpose is and how the parts achieve it but the reader really must look the diagram over until it can be seen that the gates actually do what the book says they will do If this is done faithfully with each one you will very shortly see exactly how a computer works There are only two things in our drawings there are parts that have inputs and outputs and there are lines or wires that connect outputs and inputs together When electricity comes out of the output of a gate the electricity travels through the whole wire as fast as it can go If the output of a gate is on then the electricity is on in the wire that is connected to it for as far as it goes If the output of a gate is off the whole wire is off I guess you could consider that the bit that comes out of the gate includes the whole wire as well The inputs of gates do not use up the electricity in the wire so one output may be connected to the input of one or many gates When wires are connected together this is shown by a dot where they meet on the diagram and all wires that are connected together get electricity as if they were one wire When wires cross on a diagram without a dot it means that there is no connection between them they are not touching the two bits are separate Whenever there is a choice the diagrams will show the path of the electricity moving from left to right or from the top of the page towards the bottom However there will be many exceptions to this especially later on in the book But you can always tell which way the electricity is moving in a wire by starting at an output and following it to an input Most of the diagrams in the book are very easy to follow In a few cases there will also be one of those charts that shows what the output will be for every possible combination of inputs If you have trouble following a diagram you can pencil in the ons and offs right on the page or place coins on the page and flip them so that heads means on and tails means off Unfortunately the diagram in the next chapter is probably the hardest one to follow in the whole book but once you master it youll be an expert diagram reader REMEMBER WHEN You have probably heard of computer memory and now we are going to see exactly what that is Since the only thing inside of computers is bits and the only thing that happens to bits is that they either turn on or turn off then it follows that the only thing a computer can remember is whether a bit was on or off We will now see how that is accomplished The following diagram shows one bit of computer memory It happens to be one of the neatest tricks you can do with a few gates We will examine how it works here at great length and after we understand it we will replace it with its own symbol and use it as a building block for bigger and better things It is made of only four NAND gates but its wiring is kind of special Here it is This combination as a whole has two inputs and one output I is where we input the bit that we want to remember and o is the output of the remembered bit S is an input that tells these gates when to set the memory There are also three internal wires labeled a b and c that we will have to look at to see how these parts work together Try to follow this carefully once you see that it works you will understand one of the most important and most commonly used things in a computer To see how this works start with s on and i off Since i and s go into gate 1 one input is off so a will be on Since a and s go to gate 2 both inputs are on and therefore b will be off Looking at gate 4 since b is off the output of gate 4 c will be on Since c and a are both on the output of gate 3 0 will be off O goes back down to gate 4 providing a second off input leaving c still on The important thing to note here is that with s on 0 ends up the same as i Now with s still on lets change i to on Since i and s go into gate 1 a will be off A goes to one side of both gate 2 and gate 3 therefore their outputs 0 and b must both be on O and b both on go into gate 4 and turn c off which goes back up to gate 3 providing it with a second off input leaving 0 still on The important thing to note here is the same thing we noted in the previous paragraph that with s on 0 ends up the same as i So far we have seen that when s is on you can change i on and off and 0 will change with it O will go on and off just the same as i With s on this combination is no more useful than a wire connecting i to 0 Now lets see what happens when we turn s off Look at gate 1 When s is off a will be on no matter what you do to i Now you can switch i on and off and nothing will happen The same goes for gate 2 A maybe on but s is off so b can only be on Both a and b are on and changing i does nothing Now the only thing left that matters the big question is what will 0 be If i and 0 were on befores got turned off gate 3 had both inputs off and gate 4 had both inputs on When s goes off a comes on which is one input to gate 3 But the other input is off so nothing changes 0 stays on If i and 0 were off befores got turned off gate 3 had both inputs on and gate 4 had both inputs off When s goes off b comes on which is one input to gate 4 But the other input is off so nothing changes c stays on and 0 stays off So the answer to the question of what happens to 0 when s is turned off is that it stays the way it was and it is no longer affected by i Now what do we have here With s on 0 does whatever i does With s off 0 stays the way it and i were at the last instant just befores went off Now i can change but 0 stays the way it was This combination of gates locks in the way i was at an earlier time This is how a combination of four NAND gates can remember This is only one bit of memory but this is the basic building block of all computer memory All that computer memory is is a way of preserving the way a bit was set at some point in time I hope you followed the wires and the ons and offs in this chapter Once you see exactly how this thing works you will know that these simple NAND gates can create a memory bit and I assure you that you will never wonder about it again Now that we know how this thing works we no longer need to look at that tricky internal wiring of this combination We have seen how it works and from now on we will just use this diagram to represent it I is the input bit that you want to save S is the input that allows i into the memory bit when s is on and locks it in place or sets it when s goes off O is the output of the current or saved data M stands for Memory Pretty simple eh Lets go back to our room with the funny light switches It had a NAND gate hooked up in it Lets take the NAND gate out and replace it with this new memory bit Well connect the left switch to the i wire the right switch to the s wire and the ceiling light to the o wire We could start out with everything looking the same that is the light is on but both switches are off That would mean that at some point in the past both i and s were on and s got turned off first locking the then state of i into our memory bit which then comes out at o Then i could have been switched off without affecting anything So if we walked in and decided that we wanted to turn the light off we would first try the i switch turn it on and off and nothing would happen Then we would try the s switch When we turn it on the light would go off Aha we say the s switch controls the light but it is installed upsidedown So then we turn the s switch back off expecting the light to come back on but the light remains off Now the switches are in the same position as they were when we entered the room theyre both off but now the light is off as well boy is this confusing Now I dont want to speculate on how much cursing would go on before someone figured this out but in the end they would find that when s was on the light went on and off with i and when s was off the light would stay the way it was just befores got turned off WHAT CAN WE DO WITH A BIT Now we have described a bit we have shown how to build one how to remember over time what state a bit was in at an earlier instant in time now what What do we do with it Since a bit is actually nothing more than the electricity being on or off the only actual real thing we can do with a bit is to turn lights on or off or toasters or whatever But we can also use a bit to represent something else in our lives We can take a bit and connect it to a red light and say that when this bit is on it means stop and when this bit is off you may go Or if a particular bit is on you want fries with your burger if it is off you want the burger only This is the action of using a code What is a code A code is something that tells you what something else means When something is supposed to mean something somewhere someone has to make a list of all of the states of the thing and the meanings associated with each of those states When it comes to a bit since it only can be in two different states then a bit can only mean one of two things A code for a bit would only need two meanings and one of those meanings would be associated with the bit being off and the other meaning would be associated with the bit being on This is how you assign meaning to a bit The bit does not contain any meaning in and of itself there is no room in a bit for anything other than the presence or absence of electricity Meaning is assigned to a bit by something external to the bit There is nothing about traffic or French fries in a bit we are just saying that for this bit in this place connected to a red light hanging over an intersection when it is on you must stop when it is off you may go Another bit in a cash register in a fast food restaurant means put fries in the bag when the bit is on or no fries when it is off These are two cases of someone inventing a simple twoitem code In one case the code is bit on means fries bit off means no fries in the other case bit off means go bit on means stop These two bits are the same they are just used for different purposes and someone decides what the meaning of these two bits will be The code is written down somewhere in the law books or in the restaurant managers handbook but the code is not in the bit The state of the bit merely tells someone which line of the code they are supposed to believe is true at the current moment Thats what a code is Like the spies who pass messages by using a secret code the message may be seen by other people but those other people dont have the code so they dont know what the message means Maybe one spy has a flowerpot sitting on the sill in the front window of his apartment When the pot is on the left side of the sill it means Meet me at the train station at 130 And when the flowerpot is on the right side of the sill it means No meeting today Every day the other spy walks down the street and glances up at that window to see whether he needs to go to the train station today Everyone else who walks down that street can just as easily see this message but they dont have the code so it means nothing to them Then when the two spies do meet they can pass a piece of paper that is written in another secret code They encode and decode the message using a codebook that they do not carry when they meet So if their message is intercepted by anyone else it wont mean anything to that someone else Someone who doesnt have the codebook wont have the proper meanings for the symbols on the sheet of paper A computer bit is still and will always be nothing more than a place where there is or is not electricity but when we as a society of human beings use a bit for a certain purpose we give meaning to the bit When we connect a bit to a red light and hang it over an intersection and make people study drivers handbooks before giving them drivers licenses we have given meaning to that bit Red means stop not because the bit is capable of doing anything to a vehicle traveling on the road but because we as people agree that red means stop and we seeing that bit on will stop our car in order to avoid being hit by a car traveling on the cross street and we hope that everyone else will do the same so that we may be assured that no one will hit us when it is our turn to cross the intersection So there are many things that can be done with a bit It can indicate true or false go or stop A single yes or no can be a major thing as in the answer to Will you marry me or an everyday matter such as Would you like fries with that But still there are many things that cannot be done with a bit or seem to be incompatible with the idea of bits altogether There can be many examples of yesno things in everyday life but there are many more things that are not a simple yes or no In the case of the telegraph which was indisputably just one bit how can there be more than two items in the Morse code The answer is that the ability to send and receive messages depended on the skills and the memories of the operators at both ends of the wire In the Morse Code if the key was pressed for a very short time that was called a dot and if it was pressed for a slightly longer time that was called a dash Each letter of the alphabet was assigned a unique combination of dots and or dashes and both operators studied the code memorized it and practiced using it For instance the code for the letter N was dash dot and the code for the letter C was dash dot dash dot The length of the on times were different to make dots and dashes and the lengths of the off times were different to distinguish between the time that separates dots and dashes within a letter the time that separates letters and the time that separates words You need a longer off time to keep from confusing a C with two Ns The receiving person had to recognize these as patterns that is he had to hear and remember the lengths of several on and off times until he recognized a letter The telegraph apparatus didnt have any memory at all there was never even one whole letter on the wire at any one time the pieces of letters went down the wire to be assembled into dots and dashes in the mind of the operator then into letters and then into words and sentences written on a sheet of paper So the telegraph bit achieves more than two meanings by having several individual times when there maybe ons or offs If a computer were built on the principles of the Morse code it would just have a light bulb on top of it flashing the code at us Since wed rather see whole letters words and sentences on the screen simultaneously we need something more than a single bit and this old code Even in the examples used in this chapter real traffic lights actually have three bits one for red one for yellow and one for green If you had only one bit you could just have a red light at the intersection and when it was on that would mean stop and when it was off that would mean go But when it was off you might wonder whether it was really off or whether the bulb had just burned out So using three bits is a lot more useful in this case In the real world we have already seen that computers can contain letters words sentences entire books as well as numbers pictures sounds and more And yet all of this does come down to nothing more than bits If we want our computer memory to be able to hold more than an on or off or yes or no we will have to have something more than just one bit Fortunately we can do something much more useful just by using several bits together and then making up a code or maybe several codes to assign some useful meaning to them A ROSE BY ANY OTHER NAME Before we go on we are going to introduce a change to what we call something As we know all of the bits in the computer are places where there is or is not some electricity We call these states on and off and that is exactly what they are Even though these are short words there are places where it is a lot easier clearer and simpler to use a single symbol to describe these states Fortunately were not going to invent anything tricky were just going to use two symbols you already know well the numbers zero and one From here on out we will call off o and we will call on 1 And sometimes we will still use on and off Thus the chart for our NAND gate will look like this This is very easy to understand of course but the point that needs to be made here is that the computer parts have not changed the only thing that has changed is what we as people looking at the machine are calling it Just because we call a bit a zero or one that doesnt mean that suddenly numbers have appeared and are running around inside the computer There are still no numbers or words or sounds or pictures in a computer only bits exactly as previously described We could have called them plus and minus yes and no true and false heads and tails something and nothing north and south or even Bert and Ernie But zero and one will do it This is a just a simple two item code On means l and off means 0 As a comment here there seems to be a trend among the appliance manufacturers of the world to replace the obsolete and oldfashioned terms of on and off with the modern 0 and 1 On many power switches they put a o by the off position and a 1 by the on position The first place I saw this was on a personal computer and I thought that it was a cute novelty being on a computer but now this practice has spread to cell phones coffee makers and automobile dashboards But I think that this is a mistake Do you understand that the code could just as easily have been defined as off means 1 and on means 0 The computer would work exactly the same way only the printing in the technical manuals that describe what is happening inside the computer would change When you see one of these o1 switches you have to translate it back from this very commonly used computer code into what it really means on or off So why bother You dont want to turn your coffee machine 1 you want the power ON so you can get your Java and wake up already Imagine putting these symbols on a waffle maker back in 1935 Nobody would have had any idea of what it meant It is probably just so that manufacturers dont have to have switches printed in different languages Or maybe this trend comes from an altruistic desire to educate the public into the modern fact that a 1 is the same as on but it isnt a fact its an arbitrary code EIGHT IS ENOUGH In order to be able to represent something more than simple yesno matters what we are going to do is to stack up eight bits in a single package and use them as a single unit Here is a diagram of how it is done We have taken eight of our memory bits each one still has its own data input i and its own output o but we have wired all eight of the set inputs s together Thus when the single s gets turned on and then off again all eight of these Ms will capture the states of their corresponding i s at the same time The picture on the left shows all eight Ms the one on the right is the same thing just a little simpler This assembly has a name it is called a byte thus the B in the diagram There are several conflicting explanations of exactly where this word came from but since it sounds just like the word bite you can just think of it as a whole mouthful compared with a smaller unit a bit Just to show you that computer designers do have a sense of humor when they use four bits as a unit they call it a nibble So you can eat a tiny bit of cherry pie or have a nibble or take a whole byte When we had a bit we would just say that its state was either o or 1 Now that we have a byte we will write the contents of the byte like this 0000 0000 and you can see why we switched from using offon to 01 That shows the contents of each of the eight bits in this case they are all zeros The space in the middle is just there to make it a little easier to read The left hand o or 1 would correspond to the top bit in our byte and the rightmost o or 1 would represent the bottom bit As you had better know by now a bit has two possible states that it can be in on or off If you have two bits there are four possible states that those two bits can be in Do you remember the chart we drew for the inputs of the NAND gate There were four lines on the chart one for each possible combination of the two input bits to the gate 00 01 10 and 11 Notice that the order of the bits does matter that is if you look at two bits and only ask how many bits are on there are only three possibilities no bits on one bit on or two bits on That would be calling the 10 and 01 combinations the same thing For the purpose of using multiple bits to implement a code we definitely care about the order of the bits in a byte When there are two bits we want to use all four possibilities so we have to keep the bits in order How many different possibilities are there when you use eight bits If all you have is one bit it can be in one of two states If you add a second bit the pair has twice as many states as before because the old bit has its two states while the new bit is one way and then the old bit has its two states while the new bit is the other way So two bits have four states When you add a third bit the first two have four states with the new bit off and four states with the new bit on for a total of eight states Every time you add a bit you just double the number of possible states Four bits have 16 states five have 32 six have 64 seven have 128 eight have 256 nine have 512 states and so on We are going to take eight bits and call it a byte Since a bit is a thing that has a location in space that can be in one of two states then a byte is a thing that has eight separate locations in space each of which can be on or off that are kept in the same order The byte taken as a whole is a location in space that can be in any one of 256 states at any given time and may be made to change its state over time CODES A bit could only represent yesno types of things but now that we have 256 possibilities we can look for things in our lives that are slightly more complicated One of the first things that might fit the bill is written language If you look in a book and see all of the different types of symbols that are used to print the book you will see all 26 letters of the alphabet in uppercase as well as lowercase Then there are the numbers o through 9 and there are punctuation marks like periods commas quotes question marks parentheses and several others Then there are special symbols like the at sign currency and more If you add these up 52 letters 10 numbers a few dozen for punctuation and symbols you get something like 100 different symbols that may appear printed on the pages of the average book From here on out we will use the word character to mean one of this sort of thing one of the letters numbers or other symbols that are used in written language A character can be either a letter a number a punctuation mark or any other type of symbol So we have written language with about 100 different characters and our byte with 256 possibilities maybe we can represent language with bytes Lets see how do you put an A into a byte There is nothing inherent in a byte that would associate it with a character and there is nothing inherent in a character that has anything to do with bits or bytes The byte doesnt hold shapes or pictures Dividing a character into eight parts does not find any bits The answer as before is to use a code to associate one of the possible states of the byte with something that exists in the real world The letter A will be represented by a particular pattern of 1s and 0s in the bits of a byte The byte has 256 different possible states so someone needs to sit down with pencil and paper and list out all 256 of those combinations and next to each one put one of the characters that he wants that pattern to represent Of course by the time he gets to the 101st line or so hell run out of characters so he can add every type of rarely used symbol he can think of or he can just say that the rest of the combinations will have no meaning as far as written language is concerned And so in the early days of computers each manufacturer sat down and invented a code to represent written language At some point the different companies realized that it would be beneficial if they all used the same code in case they ever wanted their companys computers to be able to communicate with another brand So they formed committees held meetings and did whatever else they needed to do to come up with a code that they could all agree on There are several versions of this code designed for different purposes and they still hold meetings today to work out agreements on various esoteric details of things But we dont need to concern ourselves with all that to see how a computer works The basic code they came up with is still in use today and I dont know of any reason why it would ever need to be changed The code has a name it is the American Standard Code for Information Interchange This is usually abbreviated to ASCII pronounced aasskey We dont need to print the whole code here but heres a sample These are 20 of the codes that they came up with the first 10 letters of the alphabet in uppercase and lowercase Each code is unique Its interesting to note the way that they arranged the codes so that the codes for uppercase and lowercase of the same letter use the same code except for one bit The third bit from the left is off for all uppercase letters and on for all lowercase letters If you wanted to put a message on your computer screen that said Hello Joe you would need nine bytes The first byte would have the code for uppercase H the second byte would have the code for lowercase e the third and fourth bytes would have the code for lowercase 1 the fifth byte would have the code for lowercase o the sixth byte would have the code for a blank space and bytes seven eight and nine would contain the codes for J o and e Notice that there is even a code for a blank space it is 0010 0000 by the way You may wonder why there needs to be a code for a blank space but that just goes to show you how dumb computers are They dont really contain sentences or words there are just a number of bytes set with the codes from the ASCII code table that represent the individual symbols that we use in written language And one of those symbols is the lack of any symbol called a space that we use to separate words That space tells us the reader that this is the end of one word and the beginning of another The computer only has bytes each of which can be in one of its 256 states Which state a byte is currently in means nothing to the computer So let us take a memory byte and set the bits to 0100 0101 That means that we have put the letter E into the byte right Well not really We have set the pattern that appears next to the letter E in the ASCII code table but there is nothing inherent in the byte that has to do with an E If Thomas Edison had been testing eight of his new experimental light bulbs and had them sitting in a row on a shelf and the first third fourth fifth and seventh light bulbs had burned out the remaining light bulbs would be a byte with this pattern But there wasnt a single person on the face of the Earth who would have looked at that row of bulbs and thought of the letter E because ASCII had not yet been invented The letter is represented by the code The only thing in the byte is the code There you have the subject of codes A computer code is something that allows you to associate each of the 256 possible patterns in a byte with something else Another language note here sometimes the word code refers to the whole list of patterns and what they represent as in This message was written with a secret code Sometimes code just refers to one of the patterns as in What code is in that byte It will be pretty obvious from the context which way it is being used BACK TO THE BYTE Do you remember the memory byte we drew a few chapters ago It was eight memory bits with their s wires all connected together Almost every time that we need to remember a byte inside a computer we also need an additional part that gets connected to the bytes output This extra part consists of eight AND gates These eight AND gates together are called an Enabler The drawing on the left shows all of the parts the drawing on the right is a simpler way to draw it The second input of all eight AND gates are connected together and given the name enable or e for short When e is off whatever comes into the Enabler goes no further because the other side of each AND gate is off thus the outputs of those gates are all going to be off When e is on the inputs go through the Enabler unchanged to the outputs o By the way when gates are used for something like this the name gate starts to make some sense An Enabler allows a byte through when the bit e is l and stops the byte when it is o So e being on is like opening a gate and e being off is like closing a gate We will take our byte and connect it to an enabler as shown in the left hand drawing To simplify once again we can draw it as shown on the right Now we have a combination that can store eight bits It captures them all at the same time and it can either keep them to itself or let them out for use somewhere else This combination of a Byte and an Enabler has a name it is called a Register thus the R in the drawing There will be a few places in this book where there are registers that never need to have their outputs turned off In those cases we will draw a register that only has a set bit and no enable bit We should probably refer to these devices as bytes but we will call them registers nonetheless Register simply means a place to record some kind of information like a hotel register where all the guests sign in or a check register where you write down each check that is written In the case of this computer part you record the state of the eight input bits This register is very limited though in that it can only hold one set of values in a hotel register there is a new line for each guest Every time you store a new state in a computer register the previous state of the eight memory bits is lost The only thing that is in there is the most recently saved value THE MAGIC BUS There are many places in a computer where eight wires are needed to connect registers together Our register for example has eight memory bits each of which have an input and an output To simplify our diagrams we will replace our eight wires with a double line So our register can look like one of these Or we can simplify and replace it with one of these Its exactly the same thing we will just save a lot of ink in our drawings and they will be easier to understand When there is a connection between two of these bundles of wires one wire of each bundle is connected to one wire of the other bundle as shown in the diagram on the left But we will simplify it and just draw it like the diagram on the right Now this grouping of eight wires is so common inside computers that it has a name It is called a bus Why is it called a bus Well it probably has to do with the old electrical term buss that means a bar of metal used as a very large wire in places like power generating plants But there is also an interesting similarity to the kind of bus that people use for transportation A bus is a vehicle that commonly travels along a predetermined route and makes many stops where people get on or off They start somewhere and the bus takes them to some other place they need to be In the world of computers a bus is simply a set of eight wires that goes to various places inside the computer Of course eight is the number of wires needed to carry a byte of information Inside the computer the contents of bytes need to get from where they are to other places so the bus goes to all these places and the design of the register allows the contents of any selected byte to get onto the bus and get off at a selected destination In the following example we have a bus and there are five registers each of which has both its input and output connected to the same bus If all of the s bits and e bits are off each register will be set the way it is and will stay that way If you want to copy the information from R1 into R4 first you turn the e bit of R1 on The data in R1 will now be on the bus and available at the inputs of all five registers If you then briefly turn the s bit of R4 on and back off the data on the bus will be captured into R4 The byte has been copied So a computer bus is a little like the bus that carries people There are a number of stops and bytes can get to where they need to go Notice that we can copy any byte into any other byte You can copy R2 into R5 or R4 into R1 The bus works in either direction The electricity put on the bus when you enable any register goes as fast as possible to the inputs of everything else on the bus You could even enable one register onto the bus and set it into two or more other registers at the same time The one thing you dont want to do is to enable the outputs of two registers onto the bus at the same time In terms of the sizes of bits you could look at it this way When the e bit of R1 gets turned on the bits in R1 now get longer they are a bigger space because they are now connected to the bus so those 8 bits now include R1 and the entire bus When the S bit of R4 gets turned on the R1 bits get even bigger because they now include R1 the bus and R4 If anything in R1 were to somehow change at this time the bus and R4 would immediately change with it When the s bit of R4 gets turned off R4 regains its status as a separate byte and when the e bit of R1 turns off the bus ceases being a part of R1 So this is a bus It is a bundle of eight wires that typically goes to many places One more thing about registers There are many places where we are going to connect the input and output of a register to the same bus so to simplify even further we can just show one bundle of wires labeled i0 meaning input and output All of the following are exactly equivalent as far as how they work The placement of the wires on the drawing maybe adjusted to make it as uncluttered as possible Another language note A byte is a location that can be in one of 256 states Sometimes we talk about moving a byte from here to there By definition bytes do not move around inside the computer The byte only refers to the location but sometimes when someone wants to refer to the current setting of the byte and they ought to say lets copy the contents of R1 into R4 they simplify and say move R1 to R4 or move this byte over there Theyre using the word byte to refer to the contents of the byte Again the context usually makes this very clear In the example above of copying the contents of R1 into R4 you may hear it described as moving a byte from R1 to R4 Technically R1and R4 are the bytes which do not move only the contents goes from place to place Also the contents do not leave the place where they came from When you are done moving a byte the from byte has not changed it doesnt lose what it had At the other end the pattern that was originally in the to byte is now gone it didnt go anywhere it was just written over by the new information The old pattern simply ceases to exist The new information is exactly the same as what is still in the first byte The byte didnt move there are still two bytes in two locations but the information in the first byte has been copied into the second byte MORE GATE COMBINATIONS Now we are going to show just two more combinations and then we will be able put together what we know so far to make the first half of a computer So dont get discouraged just a little further and well be halfway home The first combination is very simple It is just an AND gate with more than two inputs If you connect two AND gates like this diagram on the left you see that for d to be on all three inputs a b and c have to be on So this combination can simply be drawn like this diagram on the right And the chart that shows how it operates looks like this Imagine replacing input c with another AND gate then you would have a four input AND gate You could then replace any of the four inputs with another AND gate and have a five input AND gate This can be done as many times as necessary for what you are doing As you add inputs the chart will need more and more lines Every time you add another input you double the number of combinations that the inputs can have The chart we saw for the original two input AND gate had four lines one for each possibility The three input directly above has eight lines A four input AND gate will have 16 lines a five input will have 32 etc In all cases though for an AND gate only one combination will result in the output turning on that being the line where all inputs are on Here is the last combination we need to make the first half of a computer This combination is different from anything we have looked at so far in that it has more outputs than inputs Our first example has two inputs and four outputs It is not very complicated it just has two NOT gates and four AND gates In the diagram below a and b are the inputs coming in from the left Both of them are connected to NOT gates The NOT gates generate the opposite of their inputs There are four vertical wires going down the page that come from a and b and the opposites of a and b Thus for each a and b there are two wires going down the page where one of them will be on if its input is on and the other will be on if its input is off Now we put four AND gates on the right and connect each one to a different pair of the vertical wires such that each AND gate will turn on for a different one of the four possible combinations of a and b The top AND gate labeled 00 is connected to the wire that is on when a is off and the wire that is on when b is off and thus turns on when a and b are both o The next AND gate 01 is connected to the wire that is on when a is off and b so it turns on when a is o and b is 1 etc The inputs can be on in any combination both bits off one on the other on or both on None one or two on The outputs however will always have one and only one output on and the other three off The one which is on is determined by the current states of a and b This combination is called a decoder The name means that if you consider the four possible states of the two inputs as a code then the output tells you which of the codes is currently on the input Maybe its not a great name but thats what it meant to someone once and the name stuck This decoder has two inputs which means that there can be four combinations of the states of the inputs and there are four outputs one corresponding to each of the possible input combinations This can be extended If we added a third input there would then be eight possible input combinations and if we used eight three input AND gates we could build a three input eight output decoder Similarly we could build a four input 16 output decoder Decoders are named by the number of inputs X the number of outputs Like 2X4 3X8 4X16 5X32 6X64 etc Again we will simplify our drawings we wont show any of the internal parts or wiring well just have a box with a name and the inputs and outputs that we are interested in We have seen how NAND gates make NOT gates and AND gates and then NOT gates and AND gates make a Decoder It is a box full of NAND gates wired up to do something useful We know what it does one and only one of the outputs is always on and which one it is is determined by the state of the three inputs Thats all it does FIRST HALF OF THE COMPUTER Lets build something with the parts we have so far Actually we can now build fully half of whats in a computer First lets build something similar out of wood in our minds then well come back and show how to build a computer version that does pretty much the same thing You know in a hotel at the front desk on the wall behind the clerk there are a series of little wooden cubbyholes one for each room in the hotel Thats where they keep extra room keys and messages or mail for the guests Or you may have seen an old movie where someone in an old post office was sorting the mail He sits at a table with a series of cubbyholes at the back He has a pile of unsorted mail on the table picks up one at a time reads the address and puts the letter in the appropriate cubbyhole So were going to build some cubbyholes Ours will be three inches square and there will be sixteen cubbyholes high and sixteen cubbyholes across Thats a total size of four feet by four feet with a total of two hundred fifty six cubbies Now well add something that they dont have in the post office or the hotel Were going to put a large wood panel right in front of the cubbies which is twice as wide as the whole thing and in the middle it has a vertical slot that is just large enough to expose one column of 16 cubbies The panel will have wheels on the bottom so it can slide left and right to expose any one of the vertical columns of sixteen cubbies at a time and cover all of the other columns Lets take another wood panel just like the first but turn it up sideways so it is twice as high as our cubbyholes and the slot in the middle goes side to side This second panel will be mounted right in front of the first in something like a window frame so it can slide up and down exposing just one row of sixteen cubbies at a time So now we have a series of 256 cubbyholes and two slotted wooden panels in front of them that allow only one cubby at a time to be visible In each of these cubbies we will place a single slip of paper on which we will write one of the possible combinations of eight zeros and ones This cubbyhole device has 256 places to store something At any given time we can select one and only one of those places by sliding the wood panels side to side or up and down At the selected cubbyhole we can reach in and get the slip of paper and read it or replace it with another one Now we will take the gates registers and decoders that we have described and make something out of them that does pretty much the same thing as our cubbyhole device This thing will have 256 places in which to store something and we will be able to select one and only one of those places at any given time Referencing the diagram below we start with a single register Its input a is a bus that comes from somewhere else in the computer A combination of bits is placed on the bus and the sa set a bit goes 1 then o That bit pattern is now stored in this register which is one of those registers whose output is always on The first four output bits are connected to one 4X16 decoder and the other four output bits are connected to another 4X16 decoder The outputs of the two decoders are laid out in a grid pattern The wires do not touch each other but there are 16 by 16 or 256 intersections here that we will make use of soon A decoder as stated has one and only one of its outputs on at any time and the rest are off Since we have two decoders here there will be one horizontal grid wire on and one vertical grid wire on Therefore of these 256 intersections there will be only one intersection where both the horizontal and vertical wires are on Which intersection that is will change every time the value in R is changed but there will always be one where both wires are on while the other 255 will have only one on or none on At the bottom of this diagram is one bus and an s and e bit just the same as the connections that go to a register As you can see they go upwards and into the grid The diagram doesnt show it but they go up under the grid all the way to the top so that each of the 256 intersections has a bus and an s and e bit nearby There is a circle on the diagram above around one of the intersections of the grid What is in this circle is magnified in the diagram below showing that there are three AND gates and one register at each of the 256 intersections As we can see there is an AND gate x connected to the one vertical grid wire and the one horizontal grid wire at this intersection These x gates are the only things connected to the grid The rest of the connections go down to the bus and s and e bits at the bottom of the diagram Remember that there is only one intersection where both grid wires are on Therefore there are 256 of these x gates but only one of them has its output on at any given time The output of that x gate goes to one side each of two more AND gates These two gates control access to the set and enable inputs of the register at that intersection So when an x gate is off the s and e bits of that register cannot be turned on That will be the case for 255 of these registers the ones where the x gate is off But one intersection has its x gate on and its register can be set from the bus or its contents can be enabled onto the bus and sent elsewhere by using the s and e bits at the bottom of the diagram The above is the computers main memory It is half of what is necessary to build a computer It is sometimes called by different names but the most correct name comes from the fact that you can select any one of the 256 bytes one moment and then you can immediately select any other of the 256 bytes and it does not matter where the last one was or where the next one is there is no speed advantage or disadvantage to the order in which you select the bytes Because of this quality this is a good type of memory to use if you want to be able to access the bytes of memory in a random order So this type of memory is called Random Access Memory or RAM for short This is RAM It uses 257 registers 256 registers are memory storage locations one register is used to select one of the storage locations and is called the Memory Address Register or MAR for short Now that we know whats in it we can make a simplified diagram like this and an even simpler bus version This is fully half of a computer A computer has just two parts and this is one of them So now you know half of what is inside a computer Every part is made out of NAND gates That wasnt very difficult was it There is one problem here and that is that 256 bytes is a very small size for a computers RAM We maybe able to get away with it in this book but if you want a real computer its going to need a RAM with many more bytes to choose from A larger RAM can be built by providing two registers that are used to select a memory storage location This allows the use of 8X256 decoders and results in a grid with 65536 intersections and thus a RAM with 65536 different locations in which to store something Heres an idea of what it would look like Dont bother trying to count the grid lines it was only possible to fit about half of them on the printed page A bus carries one byte at a time so selecting one of the 65536 memory locations of this RAM would be a twostep process First one byte would have to be placed on the a bus and set into R0 then the second byte would have to be placed onto the a bus and set into R1 Now you could access the desired memory location with the bus and the s and e bits at the bottom of the drawing Simplifying again we have something that looks very much like our 256 byte RAM it just has one more input bit For the rest of this book we will be using the 256 byte RAM just to keep things simple If you want to imagine a computer with a larger RAM every time we send a byte to the Memory Address Register all you have to do is imagine sending two bytes instead NUMBERS We are going to return to the subject of codes for a moment Previously we looked at a code called ASCII that is used to represent written language Well numbers are used in written language too so there are ASCII codes for the digits zero through nine Earlier we saw 20 of the ASCII codes for part of the alphabet here are 10 more the codes for numbers in written language This is a very useful code but not everything that computers do has to do with written language For other tasks there are other codes that are suited better to those tasks When it comes to numbers if you use ASCII one byte can be any of the 10 digits from 0 to 9 But sometimes there is a byte that is always used to store a number and that number will never be printed or displayed on the screen In this case we can use a different code that doesnt waste any of its possible states on letters of the alphabet or anything other than numbers Since a byte has 256 possible states you can have this code represent 256 different numbers Since we want to include zero this code starts at zero and goes up to 255 Now how is this code arranged The ASCII above is not used at all this is a completely different code This code did not require any committee meetings to invent because it is the simplest and most obvious code that computers use It is the closest thing there is to a natural computer code Since this is a long chapter here is a preview of this code It consists of assigning a numeric value to each bit in the byte To use this code just turn on the bits that add up to the number you want to represent To see how this code works why it is used in computers and how those bit values were chosen we will examine the subject of numbers outside of computers There are three number systems that you are probably familiar with that we can analyze As I see it these three systems are each made up of two ideas or elements first a list of symbols and second a method for using those symbols Probably the oldest number system around is a simple thing called Tally Marks It has two symbols and The method for using these symbols is that you write down a for each of the first four things you are counting then for the fifth mark you write a across the first four You repeat this over and over as long as necessary and then when youre done you count the marks by groups of five 5 10 15 20 etc This system is very good for counting things as they pass by say your flock of sheep As each animal walks by you just scratch down one more mark you dont have to cross out 6 and write 7 This system has another advantage in that there is actually one mark for each thing that has been counted Later in the chapter we are going to do some interesting things with numbers that may get confusing so in order to keep things clear we will make use of this old system Do you remember Roman numerals It is a number system that also consists of two elements The first element is the symbols just selected letters from the alphabet I for one V for five X for ten L for fifty C for one hundred D for five hundred M for one thousand The second element is a method that allows you to represent numbers that dont have a single symbol The Roman method says that you write down multiple symbols the largest ones first and add them up except when a smaller symbol is to left of a larger one then you subtract it So II is two add one and one and TV is four subtract one from five One of the things that made this author very happy about the coming of the year 2000 was the fact that Roman numerals representing the year got a lot simpler 1999 was MCMXCIX you have to do three subtractions in your head just to read that one 2000 was simply MM The normal number system we use today also consists of two ideas but these are two very different ideas that came to us through Arabia rather than Rome The first of these ideas is also about symbols in this case 0 1 2 3 4 5 6 7 8 and 9 These digits are symbols that represent a quantity The second idea is a method that we are so used to that we use it instinctively This method says that if you write down one digit it means what it says If you write down two digits next to each other the one on the right means what it says but the one to its left means ten times what it says If you write down three digits right next to each other the one on the right means what it says the middle one means ten times what it says and the one on the left means one hundred times what it says When you want to express a number greater than 9 you do it by using multiple digits and you use this method that says that the number of positions to the left of the first digit tells you how many times you multiply it by ten before you add them up So if you have 246 apples that means that you have two hundred apples plus forty apples plus six apples So how does this work A number of any amount can be written with the digits zero through nine but when you go higher than nine you have to use two digits When you go above ninety nine you have to use three digits Above nine hundred ninety nine you go to four digits etc If you are counting upwards the numbers in any one of the positions go round and round zero to nine then zero to nine again on and on and whenever you go from nine back to zero you increase the digit to the left by 1 So you only have ten symbols but you can use more than one of them as needed and their positions with regard to each other specify their full value There is something odd about this in that the system is based on ten but there is no single symbol for ten On the other hand there is something right about this the symbols 0 through 9 do make up ten different symbols If we also had a single symbol for ten there would actually be eleven different symbols So whoever thought of this was pretty smart One of the new ideas in this Arabic system was to have a symbol for zero This is useful if you want to say that you have zero apples but it is also a necessary thing to keep the positions of the digits straight If you have 50 apples or 107 apples you need the zeros in the numbers to know what position each digit is actually in so you can multiply by ten the correct number of times Now these two ideas in the Arabic number system the digits and the method have one thing in common They both have the number ten associated with them There are ten different digits and as you add digits to the left side of a number each position is worth ten times more than the previous one In school when they first teach children about numbers they say something about our number system being based on the number ten because we have ten fingers So heres an odd question What if this number system had been invented by threetoed sloths They only have three fingers on each hand and no thumbs They would have invented a number system with only six digits 0 1 2 3 4 and 5 Could this work If you had eight apples how would you write it There is no number 8 in this system The answer is that since the first idea the digits was changed to only have six digits then the second idea the method would also have to be changed so that as you add positions to the left each one would have to be multiplied by sixes instead of tens Then this system would work As you count your apples you would say 0 1 2 3 4 5 and then what Theres no 6 for the next number Well according to the method when you want to go beyond the highest digit you go back to o and add a 1 to the left OK o 1 2 3 4 5 10 11 12 Now you have counted all of your apples What would this 12 mean It would be this many I guess youd call it eight but youd write it 12 Very odd but it does work out 1 times six plus two equals eight apples it follows the Arabic method but it is based on six instead often If you continued counting up when you got to 15 which is one times six plus five the next number would be 20 but the 2 would mean two sixes or this many And 55 would be followed by 100 The 1 in that third position would be how many 36s there were six times six This is a very odd number system but guess what you already use it in your everyday life Yes think of the way we write time or the kind of clock that shows the numbers on its face The right digit of the minutes and seconds follows our normal numbers 09 09 over and over But the left digit of the minutes and seconds only goes 05 After 59 minutes the clock goes to the next hour and 00 minutes There are 60 minutes in an hour numbered from 00 to 59 That left position never gets over 5 That position uses the number system based on six symbols 05 The hour part of the clock tells how many 60s there are though you will never see a 60 on the face of the clock And you are so used to this that you dont have to think about it When the clock says 130 you know that this is halfway between 100 and 200 you dont have to do any math in your head to figure it out Have you ever had to add time If you add 40 minutes and 40 minutes you get 80 minutes but to write that down in hours and minutes you have to figure out how many 60s there are in 80 in this case 1 then figure out how many minutes there are beyond 60 in this case 20 So you write 120 The 1 represents 60 minutes add 20 and you have your 80 again So this is pretty complicated two different number systems in the same number But you have already been using it your whole life The hour positions are even stranger On a 12 hour clock it skips zero and goes 112 AM then 112 PM On a 24 hour clock it goes from 0023 We wont try to analyze these The point we wanted to make was that you are already familiar with number systems based on numbers other than ten You could invent a number system for any amount of digits 10 or 6 like weve seen above or 3 or 14 or any number you choose But the simplest one would be if you only had 2 digits 0 and 1 How would this one work Well youd count 0 1 and then youre already out of digits so back to 0 and add 1 on the left making the next number 10 then 11 then youre out of digits again so 100 then 101 110 111 then 1000 This system is based on two so there are only two digits and as you add positions to the left each one is worth two times more than the previous one The right position means what it says the next one to the left means two times what it says the next means four times what it says the next means eight times etc When you get down to only having two possible digits you dont have to do much multiplication to figure out the total value of a position In the position that is worth eight for example there can only be a one meaning one eight or a zero meaning no eights While were at it lets imagine a very strange animal with eight fingers on each hand That animal would have invented numbers based on sixteen In their system they would be able to write ten through fifteen each with a single symbol Only when they arrived at sixteen would they get back around to 0 and need to put a 1 in the position to the left To see how this would work we need six new symbols so lets just use the first six letters of the alphabet A will mean ten B will mean eleven C will mean twelve D will mean thirteen E will mean fourteen and F will mean fifteen Only after using all sixteen symbols in the right position will we run out of symbols and the next number will be sixteen written 10 in this system If youre familiar with the pounds and ounces system of weights its sort of like this system There are 16 ounces in a pound so you know that 8 ounces is half a pound Adding 9 ounces and 9 ounces comes out to 1 pound 2 ounces Here is a chart that shows five different number systems The first column is the old tally mark system to keep it sensible Our normal 09 numbers are called the decimal system because dec means ten in some ancient language The 05 system would be called the senary system because sen means six in some other ancient language This new system with just 0 and 1 is called the binary system because bi means two also because of some ancient language This other new system the 0F system will be called the hexadecimal system because hex is another ancient word that means six and dec still means ten so its the six plus ten system Another method of naming different number systems is to call them by the number they are based on such as base 10 or base 2 etc meaning decimal or binary etc But notice that the number after the word base is written in the decimal system 2 written in binary is 10 so base 10 would mean binary if the 10 was written in binary In fact every number system would be base 10 if the 10 was written in that systems numbers So we could talk about base 2 base 6 base 10 and base 16 if we wanted to as long as we remember that those base numbers are written in decimal If we talk about binary senary decimal and hexadecimal its the same thing just possibly a little less confusing Again in our normal decimal numbers the rightmost position is the number of ones The next position to the left is the number of tens etc Each position is worth ten times the previous one In the binary system the rightmost position is also the number of ones but the next position to the left is the number of twos the next to the left is the number of fours the next is eights Each position is worth two times the amount to its right Since each position has only two possible values zero or one this is something that we could use in a byte This is the point of this chapter The binary number system is a natural match to the capabilities of computer parts We can use it as a code with off representing zero and on representing one following the Arabic number method with only two symbols In a byte we have eight bits When we use this code the bit on the right will be worth 1 when the bit is on or o when it is off The next bit to the left will be worth 2 when it is on or o when it is off The next to the left is 4 and so on with 816 32 64 and 128 In the order we normally see them the values of the eight bits look like this 128 64 32 16 8 4 2 1 In this code 0000 0001 means one 00010000 means sixteen 0001 0001 means seventeen sixteen plus one 11111111 means 255 etc In an eight bit byte we can represent a number anywhere from o to 255 This code is called the binary number code The computer works just fine with this arrangement but it is annoying for people to use Just saying what is in a byte is a problem If you have 0000 0010 you can call it zero zero zero zero zero zero one zero binary or you can mentally translate it to decimal and call it two and that is usually what is done In this book when a number is spelled out such as twelve it means 12 in our decimal system A binary 0000 0100 would be called four because that is what it works out to be in decimal Actually in the computer industry people often use hexadecimal and they just call it hex If you look at the chart above you can see that four digits of binary can be expressed by one digit of hex If you have a byte containing 00111100 you can translate it to 60 decimal or just call it 3C hex Now dont worry were not going to use hex in this book but you may have seen these types of numbers somewhere and now you know what that was all about ADDRESSES Now that we have the binary number code we can use it for various purposes in our computer One of the first places we will use it is in the Memory Address Register The pattern of bits that we put into this register will use the binary number code The bits of this number in MAR then select one of the 256 RAM storage locations The number in MAR is considered to be a number somewhere between o and 255 and thus each of the 256 RAM bytes can be considered to have an address This is fairly simple but a point needs to be made here about exactly what is meant by an address inside of a computer In a neighborhood of homes each house has an address like 125 Maple Street There is a sign at the corner that says Maple St and written on the house are the numerals 125 This is the way we normally think of addresses The point to be made here is that the houses and streets have numbers or names written on them In the computer the byte does not have any identifying information on it or contained in it It is simply the byte that gets selected when you put that number in the Memory Address Register The byte gets selected by virtue of where it is not by any other factor that is contained at that location Imagine a neighborhood of houses that had sixteen streets and sixteen houses on each street Imagine that the streets do not have signs and the houses do not have numbers written on them You would still be able to find any specific house if you were told for example to go to the fourth house on the seventh street That house still has an address that is a method of locating it it just doesnt have any identifying information at the location So a computer address is just a number that causes a certain byte to be selected when that address is placed into the Memory Address Register THE OTHER HALF OF THE COMPUTER The other half of the computer is also made ultimately of nothing but NAND gates and it probably has fewer total parts than the RAM we have built but it is not laid out so regularly and repetitively so it will take a little longer to explain We will call this half of the computer the Central Processing Unit or CPU for short because it does something with and to the bytes in RAM It processes them and we will see what that means in the next few chapters The thing that is common to both sides of the computer is the bus Here are the beginnings of the CPU The RAM is shown on the right and the bus makes a big loop between the two bus connections on the RAM The CPU starts with six registers connected to the bus These six registers are all of the places that the CPU will use to process bytes Thats not so complicated is it The big box labeled Control Section in the middle of the diagram will be examined in detail later It controls all of the set and enable bits in the CPU and the RAM The boxes with the question marks will be explained immediately following this chapter For now we are going to look at where the bytes can go within the CPU R0 R1 R2 and R3 are registers that are used as shortterm storage for bytes that are needed in the CPU Their inputs and outputs are connected to the bus They can be used for many different purposes so they are known as general purpose registers The register called TMP means temporary Its input comes from the bus and its output goes downward to one and then the other of the question marked boxes TMP has a set bit but no enable bit because we never have a reason to turn its output off The last register is called the accumulator or ACC for short This is a word that comes from the days of the old mechanical adding machines pre 1970 I guess it meant that as you added up a column of numbers it would accumulate a running total In a computer it just means that it temporarily stores a byte that comes from that big question marked box The output of ACC is then connected to our old friend the bus so it can be sent somewhere else as needed The registers in the CPU and RAM are the places where the contents of bytes come from and go to as the computer operates All movements involve enabling one register onto the bus and setting the contents of the bus into another register Now we will look at what is in those boxes with the question marks MORE GATES We have used NAND AND and NOT gates so far There are two more combination gates that we need to define The first is built like this All it does is to NOT the two inputs to one of our good old NAND gates Here is the chart for it showing the intermediate wires so it is easy to follow In this case when both inputs are off the output is off but if either a OR b is on or both then the output will be on So it has another very simple name it is called the OR gate Instead of drawing all the parts it has its own diagram shaped something like a shield The diagram and chart look like this Like the AND gate you can build OR gates with more than two inputs Just add another OR gate in place of one of the inputs and you will then have three inputs any one of which will turn the output on Also like the AND gate every time you add an input the number of lines on the chart will double With the OR gate only the line that has all inputs off will have the output off All the rest of the lines will show the output being on The last combination gate we need here takes five gates to make but what it ultimately does is quite simple Similar to the OR gate the output is on when either input is on but in this version the output goes back off if both inputs are on So it is called an Exclusive OR gate or XOR gate for short The output is on if either OR the other input is on exclusively Only if it is OR not if it is AND Another way to look it at it is the output comes on if one and only one input is on Still another way to look at it is the output is off if the inputs are the same and on if the inputs are different The simplified diagram looks similar to an OR gate but it has a double curved line on the input side The diagram and chart look like this We now have four kinds of gates that take two inputs and make one output They are NAND AND OR and XOR Here is a chart that makes it pretty simple For the four possible input combinations of a and b each type of gate has its own set of output states and the names of the gates can help you remember which is which In spite of the fact that everything in the computer is made out of NAND gates we are not going to be using any NAND gates by themselves in this computer Now that we have used them to build AND OR XOR and NOT gates and the memory bit we are done with the NAND gate Thank you Mr NAND gate bye bye for now MESSING WITH BYTES Individual gates operate on bits Two bits in one bit out But the RAM stores and retrieves a byte at a time And the bus moves a byte at a time Here in the CPU we want to be able to work on a whole byte at one time We want some gates that affect an entire byte In the chapter on the bus we saw how the contents of a byte can be copied from one register to another This is usually referred to as moving a byte Now we are going to see some variations on this First we will see three ways that we can change the contents of a byte as it moves from one register to another Second we will see four ways that we can take the contents of two bytes and have them interact with each other to create the contents for a third byte These are all of the things that computers actually do to bytes All things ultimately come down to these seven operations THE LEFT AND RIGHT SHIFTERS The shifter is very easy to build It doesnt use any gates at all it just wires up the bus a bit oddly It is done like this This shows two registers connected by a right shifter The shifter is just the wires between the two registers When the e bit of R1 is turned on and the s bit of R2 is turned on and then off all of the bits in R1 are copied into R2 but they are shifted over one position The one at the bottom shift out can be connected to some other bit in the computer but is often connected back to the one on the top shift in and when that is done the rightmost bit wraps around to the leftmost bit at the other end of the byte A right shifter will change 0100 0010 to 0010 0001 If shift out is connected to shift in a right shift will change 0001 1001 to 1000 1100 A left shifter will change 0100 0010 to 1000 0100 The left shifter is wired up like so Once again we have bus versions of these drawings They each have an i and o bus and also one input and output bit like this Now of what use is this The minds of programmers have come up with all sorts of things but here is an interesting one Assume that you are using the binary number code You have the number 0000 0110 in R1 That comes out to the decimal number 6 Now shift that code left into R2 R2 will then be 0000 1100 This comes out to the decimal number 12 What do you know we have just multiplied the number by 2 This is the basis of how multiplication is done in our computer How you multiply by something other than 2 will be seen later but this is how simple it is just shift the bits This is similar to something we do with decimal numbers If you want to multiply something by ten you just add a zero to the right side effectively shifting each digit left one position In the binary system this only results in multiplying by two because two is what the system is based on So thats the shifter no gates at all THE NOTTER This device connects two registers with eight NOT gates Each bit will be changed to its opposite If you start with 0110 1000 you will end up with 1001 0111 This operation is used for many purposes the first being in some arithmetic functions We will see exactly how this works soon after we describe a few other things Another name for a NOT gate is an inverter because it makes the opposite of what you give it turns it up side down or inverts it Since the input and the output are both eight wires well simplify by using our bus type picture THE ANDER The ANDer takes two input bytes and ANDs each bit of those two into a third byte As you can see the eight bits of the a input bus are connected to the upper side of eight AND gates The eight bits of the b input bus are connected to the lower side of the same eight AND gates The outputs of the eight AND gates form the bus output c of this assembly With this we can AND two bytes together to form a third byte There are many uses for this For example you can make sure that an ASCII letter code is uppercase If you have the code for the letter e in R0 0110 0101 you could put the bit pattern 1101 1111 into R1 and then AND R1 and R0 and put the answer back into R0 All of the bits that were on in R0 will be copied back to R0 except for the third bit Whether the third bit had been on or off before it will now be off R0 will now contain 0100 0101 the ASCII code for E This works for all ASCII letter codes because of the way ASCII is designed Here is a simpler bus type picture for the ANDer THE ORER The ORer takes two input bytes and ORs each bit of those two into a third byte As you can see the eight bits of the a input bus are connected to the upper side of eight OR gates The eight bits of the b input bus are connected to the lower side of the same eight OR gates The outputs of the eight OR gates are the bus output c of this assembly With this we can OR two bytes together to form a third byte What is the use of this There are many but here is one of them Say you have the ASCII code for the letter E in R0 0100 0101 If you want to make this letter be lowercase you could put the bit pattern 0010 0000 into R1 and then OR R0 and R1 and put the answer back into R0 What will happen All of the bits of R0 will be copied back into R0 as they were except the third bit will now be on no matter what it had been R0 will now be 0110 0101 the ASCII code for e This will work no matter what ASCII letter code was in R0 because of the way ASCII was designed Here is a simpler bus type picture for the ORer THE EXCLUSIVE ORER The XORer takes two input bytes and XORs each bit of those two into a third byte As you can see the eight bits of the a input bus are connected to the upper side of eight XOR gates The eight bits of the b input bus are connected to the lower side of the same eight XOR gates The outputs of the eight XOR gates are the bus output c of this assembly With this we can XOR two bytes together to form a third byte What is the use of this Again imaginative people have come up with many of uses But here is one of them Say you have one code in R1 and another code in R2 You want to find out if those two codes are the same So you XOR R1 and R2 into R1 If R1 and R2 contained the same patterns then R1 will now be all zeros It doesnt matter what pattern of 0s and 1s was in R1 if R2 contained the same pattern after an XOR R1 will be all zeros Since both of the inputs and the output are all eight wires well simplify by using our bus type picture THE ADDER This is a combination of gates that is surprisingly simple considering what it does In our binary number system we have numbers in the range of 0 to 255 represented in a byte If you think about how addition is done with two of our regular decimal numbers you start by adding the two numbers in the right column Since the two numbers could each be anywhere from 0 to 9 the sum of these two will be somewhere from 0 to 18 If the answer is anywhere from 0 to 9 you write it down below the two numbers If the answer is from 10 to 18 you write down the right digit and carry the 1 to add to the next column to the left In the binary number system it is actually much simpler If you do the same type of addition in binary the two numbers in the right column can each only be 0 or 1 Thus the only possible answers for adding the right column of two binary numbers will be 0 1 or 10 zero one or two If you add 00 you get 0 10 or 01 you get 111 you get o in the right column and carry 1 to the column to the left The gates we have described can easily do this An XOR of the two bits will tell us what the right column answer should be and an AND of the two bits will tell us whether we need to carry a 1 to the column on the left If one bit is on and the other one is off that is we are adding a 1 and a 0 the answer for the right column will be 1 If both numbers are 1 or both numbers are o the right column will be o The AND gate turns on only in the case where both input numbers are 1 So we have added the right column easily Now we want to add the next column to the left Should be the same right There are two bits that could be 0 or 1 but this time we also have the possibility of a carry from the previous column So its not the same this time we are really adding three numbers the two bits in this column plus the possible carry from the previous column When adding three bits the possible answers are 0 1 10 or 11 zero one two or three It is more complex but not impossible Here is the combination that does it The left XOR tells us if a and b are different If they are and carry in is off or if a and b are the same and carry in is on then the right XOR will generate 1 as the sum for the current column The lower AND gate will turn on carry out if both inputs are on The upper AND gate will turn on carry out if carry in and one of the inputs are on This is the simplicity of how computers do addition Now that we see that it works we can make a simpler picture of it To make an adder that adds two bytes together we need a one bit adder for each bit of the bytes with the carry output of each bit connected to the carry input of the next Notice that every bit has a carry in even the first bit the right column This is used when we want to add numbers that can be larger than 255 And the simplified picture of it with bus inputs and output The carry output bit of the leftmost top column will turn on if the sum of the two numbers is greater than 255 and this bit will be used elsewhere in the computer This is how computers do addition just five gates per bit and the computer can do arithmetic THE COMPARATOR AND ZERO All of the things we have described above take one or two bytes as input and generate one byte of output The shifters and the adder also generate one extra bit of output that is related to their output byte The comparator only generates two bits of output not a whole byte The comparator is actually built right into the XORer because it can make use of the gates that are already there The XORer generates its byte of output and the comparator generates its two bits These two functions are not really related to each other it just happens to be easy to build it this way What we want the comparator to do is to find out whether the two bytes on the input bus are exactly equal and if not whether the one on the a bus is larger according to the binary number system The equal thing is pretty simple XOR gates turn off when the inputs are the same so if all of the XOR gates are off then the inputs are equal To determine the larger of two binary numbers is a little trickier You have to start with the two top bits and if one is on and the other is off then the one that is on is the larger number If they are the same then you have to check the next lower pair of bits etc until you find a pair where they are different But once you do find a pair that are different you dont want to check any more bits For example 0010 0000 32 is larger than 0001 1111 31 The first two bits are the same in both bytes The third bit is on in the first byte and off in the second and therefore the first byte is larger Although the rest of the bits are on in the second byte their total is less than the one bit that is on in the first byte That is what we want to have happen and it takes five gates times eight positions to accomplish it Since we are starting with the XORer we will add four more gates to each position as shown in this diagram Remember in the adder we had a carry bit that passed from the lowest bit position up through to the highest bit In the comparator we have two bits that pass down from the highest bit position to the lowest Here is one bit of the comparator You can see the original XOR gate labeled 1 connected up to one bit of each input bus on the left and generating one bit for the output bus on the right If the output of gate 1 is on that means that a and b are different or unequal We add gate 2 which will turn on when a and b are equal If gate 2 is on at every position then gate 3 will be on at every position as well and the bit that comes out of the bottom tells us that the two input bytes are equal Gate 4 turns on if three things are true 1 Bits a and b are different 2 Bit a is the one that is on 3 All bits above this point have been equal When gate 4 turns on it turns gate 5 on and that turns on every other gate 5 below this point and therefore the a larger output of the comparator When byte b is the larger one both the equal bit and the a larger bit will be off You stack up eight of these bit comparators like the following diagram with a 1 and 0 connected to the top one to get it started You still have the XOR function coming out at c and now the two comparator bits at the bottom Simplifying again we will go back to the bustype XOR diagram and just add the two new output bits of the comparator There is one more thing that we are going to need in our computer that gives us another bit of information This is a simple gate combination that takes a whole byte as input and generates only one bit as output The output bit turns on when all of the bits in the byte are off In other words the output bit tells us when the contents of the byte is all zeros It is simply an eight input OR gate and a NOT gate When any of the inputs to the OR gate are on its output will be on and the output of the NOT gate will be off Only when all eight inputs of the OR are off and its output is therefore off will the output of the NOT gate be on The simpler bus representation is shown on the right LOGIC The subject of thinking has been the object of much study and speculation through the ages There was a man in ancient Greece named Aristotle who did a lot of work in this area He must have met a lot of illogical people in his life because he invented a subject that was supposed to help people think more sensibly One of his ideas was that if you have two facts you may be able to derive a third fact from the first two In school they sometimes give tests that present two facts then they give you a third fact and ask whether the third fact is logical based on the first two You may remember questions such as If Joe is older than Bill And Fred is older than Joe Then Fred is older than Bill True or False Or Children like candy Jane is a child Therefore Jane likes candy True or False Aristotle called his study of this sort of thing Logic The only relevance this has to our discussion of computers is this word logic Aristotles logic involved two facts making a third fact Many of our computer parts such as AND gates take two bits and make a third bit or eight AND gates take two bytes and make a third byte And so the things that these gates do has come to be known as logic There maybe AND logic and OR logic and XOR logic but the general term for all of them is logic ANDing ORing and XORing take two bytes to make a third so they fit this definition of logic pretty well Shifting and NOTing have also come to be known as logic even though they only take one byte of input to generate their output The ADDer although it is has two inputs and is also very logical somehow is not known to be in the category of logic it is in its own category arithmetic So all of the ways that we have described above of doing things to bytes come under the heading of arithmetic and logic THE ARITHMETIC AND LOGIC UNIT Now we have built seven different devices that can do arithmetic or logic on bytes of data We are going take all seven of these devices put them together in one unit and provide a method of selecting which one of these devices we want to use at any given time This is called the Arithmetic and Logic Unit or ALU for short All seven devices are connected to input a the devices that have two inputs are also connected to input b All seven devices are connected to the inputs at all times but each output is attached to one of those enablers The wires that turn the enablers on are connected to the outputs of a decoder thus only one enabler can be on at a given time Seven of the decoders outputs enable a single device to continue on to the common output c The eighth output of the decoder is used when you dont want to select any device at all The three input wires to the decoder are labeled op because they choose the desired operation The one little complication here is the carry bits from the adder and the shift in and shift out bits from the shifters These are used in very similar ways and so from here on out we will refer to all of them as carry bits The adder and both shifters take carry as an input and generate carry as an output So the three carry inputs are connected to a single ALU input and one of the three outputs is selected along with the bus output of its device Look at the rightmost output of the 3X8 decoder above and see that it enables both the adder bus and the adder carry bit What do we have here It is a box that has two bus inputs one bus output and four other bits in and four other bits out Three of the input bits select which operation will take place between the input and output buses Again now that we know whats in it and how it works we dont need to show all of its parts Here is a simplified way to draw it Notice that the three single bit inputs labeled op above can have eight different combinations Seven of those combinations select one of the devices described previously The eighth combination does not select any output byte but the a larger and equal bits still work as they do at all times so this is the code to choose if you only want to do a comparison The combination of bits at op mean something That sounds like another code Yes here is a threebit code that we will make use of soon The Arithmetic and Logic Unit is the very center the heart of the computer This is where all of the action happens Ill bet this is a lot less complicated than you thought MORE OF THE PROCESSOR There is one more little device we need It is a very simple thing it has a bus input a bus output and one other input bit It is very similar to an enabler Seven of the bits go through AND gates and one of them goes through an OR gate The single bit input determines what happens when a byte tries to pass through this device When the bus 1 bit is off all of the bits of the input bus pass through to the output bus unchanged When the bus 1 bit is on the input byte is ignored and the output byte will be 0000 0001 which is the number l in binary We will call this device a bus 1 because it will place the number 1 on a bus when we need it Now we can put this bus 1 and the ALU into the CPU We will change where the wires go in and out of the ALU so it fits our diagram better The bus inputs come in the top the bus output comes out the bottom and all of the input and output bits are on the right The output of the ALU is connected to ACC ACC receives and temporarily stores the result of the most recent ALU operation The output of ACC is then connected to the bus so its contents can be sent somewhere else as needed When we want to do a one input ALU operation we have to set the three op bits of the ALU to the desired operation enable the register we want onto the bus and set the answer into ACC For a two input ALU operation there are two steps First we enable one of the registers onto the bus and set it into TMP Then we enable the second register onto the bus choose the ALU operation and set the answer into ACC As you can see we can now move bytes of data to and from RAM to and from the Registers through the ALU to ACC and from there into a register or RAM if we turn the appropriate enable and set bits on and off at the right time This is what happens inside of computers Thats not so complicated is it There is only one thing missing here and that has to do with all of these control bits on the registers ALU and RAM The RAM has three control bits one to set MAR one to set the currently selected byte in one to enable the currently selected byte out Each of the registers R0 R1 R2 R3 and ACC have a set and an enable bit TMP only has a set bit bus 1 has a control bit and the ALU has those three op bits that select the desired operation We need something that will turn all of these control bits on and off at the appropriate times so we can do something that is useful Now it is time to look into that box labeled Control Section THE CLOCK We need to turn the appropriate control bits on and off at the appropriate times We will look at the appropriate bits later first we will look at the appropriate times Here is a new kind of drawing we will call it a graph It shows how one bit changes over time Time starts on the left and marches forward to the right The line on the graph has two possible positions up means the bit is on and down means the bit is off This graph shows bit X going on and off on and off regularly There could be a time scale on the bottom to show how fast this is happening If the whole width of the page represented one second then bit X would be going on and off about eight times per second But we wont need a time scale in these graphs as we will only be concerned with the relative timing between two or more bits The speed in an actual computer will be very fast such as the bit going on and off a billion times per second When something repeats some action regularly one of those actions individually is called a cycle The graph above shows about eight cycles You can say that from one time the bit turns on to the next time the bit turns on is a cycle or you can say that from the middle of the off time to the middle of the next off time is the cycle as long as the cycle starts at one point in time when the bit is at some stage of its activity and continues until the bit gets back to the same stage of the activity again The word Cycle comes from the word circle so when the bit comes full circle that is one cycle There was a scientist who lived in Germany in the 1800s who did some of the early research that led up to radio His name was Heinrich Hertz and among other things he studied electricity that was going on and off very quickly Some decades after his death it was decided to use his name to describe how fast electricity was going on and off or how many cycles occurred per second Thus one Hertz or Hz for short means that the electricity is going on and off once per second 500 Hz means 500 times per second For faster speeds we run into those ancient languages again and one thousand times per second is called a kilohertz or kHz for short Going on and off a million times per second is called a megahertz or mHz for short and a billion times is called a gigahertz or gHz for short Every computer has one special bit All other bits in a computer come from somewhere they are set on and off by other bits or switches This one special bit turns on and off all by itself But there is nothing mysterious about it it just goes on and off very regularly and very quickly This special bit is built very simply like this This seems a silly thing to do Just connect a NOT gates output back to its input What will this do Well if you start with the output on the electricity travels back to the input where it enters the gate which turns the output off which travels back to the input which turns the output on Yes this gate will just go on and off as quickly as possible This will actually be too fast to be used for anything and so it can be slowed down just by lengthening the wire that makes the loop The simplified diagram shows this to be the one special bit in the computer that has an output but does not have any inputs This bit has a name It is called the clock Now we usually think of a clock as a thing with a dial and hands or some numbers on a screen and we have seen such clocks in the corner of a computer screen Unfortunately someone named this type of bit a clock and the name stuck with the computer pioneers It could have been called the drumbeat or the pacesetter or the heart or the rhythm section but they called it a clock That is what we will mean when we say clock throughout the rest of this book I guess its a clock that ticks but doesnt have a dial If we want to talk about the type of clock that tells you what time it is we will call it a time of day clock or TOD clock for short But the word clock will mean this type of bit How quickly does this clock go on and off These days it is well over a billion times per second or several gigahertz This is one of the main characteristics that computer companies tell you about to show you how great their computers are When you see computers for sale the speed that they advertise is the speed of its clock The faster a computer is the more expensive it is because it can do more things in one second It is the speed of this single bit going on and off that sets the tempo for the whole computer To move data via the bus we need first to enable the output of one and only one register so that its electricity can travel through the bus to the inputs of other registers Then while the data is on the bus we want to turn the set bit of the destination register on and off Since the destination register captures the state of the bus at the instant that the set bit goes off we want to make sure that it goes off before we turn off the enable bit at the first register to make sure that there are no problems Let us first attach a length of wire to the output of the clock This will delay the electricity slightly We want it delayed about one quarter of a cycle If we show the original clock output clk and the delayed clock output clk d on a graph they will look like this Now were going to do something fairly simple We will take the original clock and the delayed clock and both AND them and OR them to create two new bits like so One of the new bits is on when either clk or clk d are on and the other new bit is on only when both clk and clk d are on The graph of the inputs and outputs of the AND and OR gates is shown here They are both still going on and off regularly but one of them is on for longer than it is off and the other one is off for longer than it is on The on time of the second is right in the middle of the on time of the first Notice that they have names clk e which stands for clock enable and clk s which stands for clock set And what do you know these two bits have the perfect timing to move a byte of data from one register across the bus and into another register Just connect clk e to the enable bit of the from register and connect clk s to the set bit of the to register Here is a single onoff cycle of these two bits If you look at the timing here this meets our requirements of needing to first enable the output of a register and then after the data has a little time to travel down the bus to turn the set bit of the destination register on and off before turning the enable bit off at the first register Of course these clock bits cannot just be connected directly to every register There must be other gates in between that only allow one register to get an enable at any one time and only the desired registers to receive a set But all enables and sets ultimately come from these two bits because they have the right timing Since we will use clk clk e and clk s throughout the computer this is the diagram we will use to show the clock DOING SOMETHING USEFUL Lets say that we want to do something useful like adding one number to another number We have a number in R0 and there is another number in R1 that we want to add to the number in R0 The processor we have built so far has all of the connections to do this addition but it will take more than one clock cycle to do it In the first clock cycle we can enable R1 onto the bus and set it into TMP In the second cycle we can enable R0 onto the bus set the ALU to ADD and set the answer into ACC In the third cycle we can enable ACC onto the bus and set it into Ro We now have the old value of R0 plus R1 in R0 Perhaps this doesnt seem very useful but it is one of the kind of small steps that computers do Many such small steps make the computer seem to be able to do very complex things Thus we see that for the processor to do something useful it takes several steps It needs to be able to do actions in a sequence We need another piece inside this Control Section STEP BY STEP This chapter introduces a new part called the Stepper First we will describe the completed stepper showing exactly what it does After that we will see exactly how it is built If you happen to trust your author enough to believe that such a stepper can be built out of gates and youre in such a hurry that you want to skip the how it is built part of the chapter you might still understand the computer Here is a complete stepper It has two inputs One is called clk because this is where we connect a bit that is going on and off such as our original clock bit The other input is called reset which is used to return the stepper back to step one For outputs it has a number of bits each of which will come on for one complete clock cycle and then turn off one after the other The output labeled Step 1 turns on for one clock cycle then Step 2 for the next clock cycle etc A stepper can be built to have as many steps as needed for any particular task you want to do In the case of this computer that we are building seven steps are sufficient When the last step 7 turns on it stays on and the stepper doesnt do anything else until the reset bit is turned on briefly at which time the steps start over again beginning with Step 1 Here is a graph of the input clk bit and the outputs of a sevenstep stepper Here is how the stepper is built It is done using some of the same memory bits that we used to make registers but they are arranged very differently We are not going to store anything in these bits we are going to use them to create a series of steps The stepper consists of several memory bits connected in a string with the output of one connected to the input of the next Here is a diagram that shows most of the stepper First look at the series of M memory bits just like the ones that we used earlier in the book In this picture there are twelve of them connected together with the output of one connected to the input of the next all the way down the line The input to the first bit on the left is connected to a place where the electricity is always on so when the set bit of that M comes on that M will receive that on state and pass it through to its output If you look at the set bits of these Ms you will see that the set bits of the even numbered Ms are connected to clk and the set bits of the odd numbered Ms are connected to the same clock after it goes through a NOT gate This new bit that is made by passing clk through a NOT gate can be called not clk and we can show both on this graph So what will happen with this bunch of gates If you assume that all of the Ms start in the off state and then start clk ticking here is what it will do The first time clk comes on nothing will happen because the set bit of the first M is connected to not clk which is off when clk is on When clk goes off not clk turns on and the first M will come on but nothing will happen at the second M because its set bit is connected to clk which is now off When clk comes back on the second M will now come on As the clock ticks the on that enters the first memory bit will step down the line one bit for each time the clock goes on and one bit for each time the clock goes off Thus two bits come on for each clock cycle Now turning to the full stepper diagram below step 1 comes from a NOT gate connected to the output of the second M Since all Ms start off step 1 will be on until the second M comes on at which time step l will be over For the remaining steps each one will last from the time its left side M turns on until the time its right side M turns on The AND gates for steps 26 have both inputs on when the left M is on and the right M is off If we connect the output of one M and the NOT of the output of an M two spaces farther on to an AND gate its output will be on for one complete clock cycle Each one comes on when its left input has come on but its right input has not yet come on This gives us a series of bits that each come on for one clock cycle and then turn off The only thing missing here is that the M bits come on and stay on Once they are all on there is no more action despite the clocks continued ticking So we need a way to reset them all off so we can start over again We have to have a way to turn off the input to the first M and then turn on all of the set bits at the same time When that happens the off at the input to the first M will travel through all of the Ms as fast as it can go We will add a new input called reset which will accomplish these things When we turn reset on it makes the input to the first M bit a zero and turns on all of the sets at the same time so that the zero can travel down the line of Ms very quickly Reset is also ORed with step l so that step l turns on immediately Now all of the bits are off and we have started another sequence Reset only needs to be turned on for a fraction of one clock cycle To recap this is a stepper It has two inputs a clock and a reset For outputs it has a number of bits each of which will come on for one clock cycle We can actually make this as long as needed but for the purposes of this book a seven stage stepper will be sufficient There will be only one stepper in our computer we will represent it with this simplified diagram We have relocated the Reset bit to the right side of the diagram and connected it to the last step 7 so that the stepper will automatically reset itself Step 7 will not be on for very long however because it shuts itself off as soon as the zero can get through the string of Ms This means that step 7 will not last long enough to be used for one of our data transfers over the bus All of the things we want to accomplish will take place in steps 1 through 6 EVERYTHINGS UNDER CONTROL With our clock we have a drumbeat to make things go It has a basic output and two more that are designed to facilitate the movement of the contents of registers from one to another With the stepper we have a series of bits that come on one after another each for one clock cycle Remember the diagram of the CPU we saw a few chapters back It showed the bus the ALU six registers and even the other half of the computer the RAM all connected up pretty neatly At least all of the bus connections were there But all the registers the RAM the Bus 1 and the ALU are controlled by wires that come from that mysterious box labeled Control Section that we know nothing about yet Now it is time to look inside that box This drawing is the beginning of the control section of the computer At the top are the clock and the stepper Then all of the control bits from the registers and RAM have been brought here together in one place with all of the enable bits on the left and all of the set bits on the right Then we have connected the output of an AND gate to each enable and each set bit One input of each AND gate is connected to either clk e for the enables on the left or clk s for the sets on the right Thus if we use the other input of those AND gates to select any of those registers the enable bit of all of the items on the left will never be turned on except during clk e time Similarly on the right the set bit of any of those registers will only be turned on during clk s time This is sort of a switchboard Everything we need to make the computer do something is right here in one place All we need to do is connect some control bits to some steps in an intelligent manner and something useful will happen DOING SOMETHING USEFUL REVISITED Now that we have the beginning of our control section we can just add a few wires and we will be able to do the simple addition we postulated earlier that of adding R1 to R0 All we have to do to do something useful like adding R1 to R0 is to connect a few wires in the middle as shown in this diagram with steps four five and six Each step causes something to happen to some of the parts that are shown in the CPU diagram Each step is connected to one enable on the left and one set on the right and therefore causes one part to connect its output to the bus and another part to save what now appears at its input Step four is wired to R1 enable and TMP set Step five is wired to R0 enable and ACC set The ALU op bits do not need any connections since the op code for ADD is 000 Step six is wired to ACC enable and R0 set During step four R1 is enabled and TMP is set The contents of R1 travel across the bus in the CPU diagram and are captured by TMP During step five R0 is enabled and ACC is set If we wanted to do something other than ADD this is the step where we would turn on the appropriate ALU op code bits During step six ACC is enabled and R0 is set Here is a graph of the steps showing when each register gets enabled and set R0 now contains the sum of the original contents of R0 plus R1 This is how the computer makes things happen in a tightly controlled ballet of bits and bytes moving around inside the machine In step seven the stepper is reset to step 1 where the process repeats Of course it is not very useful to just do this addition over and over again even if you start out with the number 1 in both R0 and R1 R0 will get up to 255 pretty quickly If the clock in our computer ticks one billion times every second otherwise known as one gigahertz and even if we use multiple clock cycles to do something useful like this that means that the computer can do something like this hundreds of millions of times in one second But we dont want to just add R1 to R0 over and over again Perhaps now that we have added R1 to R0 we want to store that new number to a particular address in RAM and R2 happens to have that address in it Again our processor has all of the connections necessary to do this and again it will take more than one clock cycle to do it In step 4 we can move R2 across the bus to MAR In step 5 we can move R0 across the bus to RAM Thats all that is needed just two clock cycles and were done The wiring for this operation is simpler than the other one just two enables and two sets There are many combinations of things that we can do with the RAM the six registers and the ALU We could get a byte from RAM and move it to any of the four registers we could move any one or two of the registers through the ALU and ADD them AND them OR them XOR them etc We need a way for our CPU to do one thing one time and a different thing the next time The control section needs something to tell it what to do in each sequence WHATS NEXT Now heres a scary idea Imagine that the job that an employee does at a fast food restaurant gets broken down into its individual elements Walk to the counter say May I take your order listen to the answer press the cheeseburger button on the cash register etc Now lets say that there are 256 or less individual actions involved in the job of working at such an establishment You could then invent a code that would associate one of the states of a byte with each of the individual activities of an employee Then you could express the sequence of an employees actions as a sequence of bytes First we make up a code table We write some codes down the left side of the page Then we decide what we want those codes to mean and write those meanings next to the codes Now we have a list of all of the possible actions that an employee might take and a code that represents each one of them 0000 0000 Walk to the counter 0000 0001 Say May I take your order 0000 0010 Listen to the answer 0000 0011 Press the cheeseburger button 0000 0100 Press the fries button 0000 0101 Press the milk button 0000 0110 Press the total button 0000 0111 Collect the money 0000 1000 Give the customer the change 0000 1001 Open an empty bag 0000 1010 Place a cheeseburger in the bag 0000 1011 Place fries in the bag 0000 1100 Place a milk container in the bag 0000 1101 Hand the bag to the customer 1000 0000 Go to the step number in the right 6 bits 0100 0000 If yes go to the step number in the right 6 bits 0001 0000 Go home Now if we want to describe how the employee is supposed to act we write a sequence of events that he should follow 1 0000 0000 Walk to the counter 2 0000 0001 Say May I take your order 3 0100 0010 If customer is not answering go to step 2 4 0000 0010 Listen to the answer 5 0100 0111 If customer doesnt say cheeseburger go to step 7 6 0000 0011 Press the cheeseburger button 7 0100 1001 If customer does not say fries go to step 9 8 0000 0100 Press the fries button 9 0100 1011 If customer does not say milk go to step 11 10 0000 0101 Press the milk button 11 0100 1101 If the customer says thats all go to step 13 12 1000 0100 Go back to step 4 13 0000 0110 Press the total button 14 0000 0111 Collect the money 15 0000 1000 Make change and give it to the customer 16 0000 1001 Open an empty bag 17 0101 0011 If order doesnt include cheeseburger go to step 19 18 0000 1010 Place a cheeseburger in the bag 19 0101 0110 If order does not include fries go to step 22 21 0000 1011 Place fries in the bag 22 0101 1000 If order does not include milk go to step 24 23 0000 1100 Place a milk container in the bag 24 0000 1101 Hand the bag to the customer 25 0101 1011 If it is quitting time go to step 27 26 1000 0001 Go back to step 1 27 0001 0000 Go home I hope nobody ever tries to make the employees of a fast food restaurant learn a code like this People dont take well to being so mechanized But maybe someone will try to staff one of these restaurants with robots someday In that case the robots would probably work better using this sort of a code And our computer might be able to understand a code like this THE FIRST GREAT INVENTION What we need is some way to do different operations from one stepper sequence to the next How could we have it wired up one way for one sequence and then a different way for the next sequence The answer of course is to use more gates The wiring for one operation can be connected or disconnected with AND gates and the wiring for a different operation can be connected or disconnected with some more AND gates And there could be a third and fourth possibility or more As long as only one of those operations is connected at one time this will work fine Now we have several different operations that can be done but how do you select which one will be done The title of this chapter is The First Great Invention so what is the invention The invention is that we will have a series of instructions in RAM that will tell the CPU what to do We need three things to make this work The first part of the invention is that we are going to add another register to the CPU This register will be called the Instruction Register or IR for short The bits from this register will instruct the CPU what to do The IR gets its input from the bus and its output goes into the control section of the CPU where the bits select one of several possible operations The second part of the invention is another register in the CPU called the Instruction Address Register or IAR for short This register has its input and output connected to the bus just like the general purpose registers but this one only has one purpose and that is to store the RAM address of the next instruction that we want to move into the IR If the IAR contains 0000 1010 10 decimal then the next instruction that will be moved to the IR is the byte residing at RAM address ten The third part of the invention is some wiring in the control section that uses the stepper to move the desired instruction from RAM to the IR add 1 to the address in the IAR and do the action called for by the instruction that has been put in the IR When that instruction is complete the stepper starts over again but now the IAR has had 1 added to it so when it gets that instruction from RAM it will be a different instruction that was located at the following RAM address The result of these three parts is a great invention This is what allows us to make the computer do many different things Our bus ALU RAM and registers make many combinations possible The contents of the IR will determine what registers are sent to where and what kind of arithmetic or logic will be done upon them All we have to do is to place a series of bytes in RAM that represent a series of things that we want to do one after another This series of bytes residing in RAM that the CPU is going to make use of is called a program The basic thing that happens here is that the CPU fetches an instruction from RAM and then executes the instruction Then it fetches the next one and executes it This happens over and over and over millions or billions of times every second This is the simplicity of what a computer does Someone puts a program in RAM and that program if intelligently designed makes the computer do something that people find useful The stepper in this computer has seven steps The purpose of step 7 is only to reset the stepper back to step 1 So there are six steps during which the CPU does small things Each step lasts for one clock cycle The six steps taken as a whole is called an Instruction Cycle It takes six steps for the CPU to do all of the actions necessary to fetch and execute one instruction If we assume that our clock ticks at one gigahertz then our computer will be able to execute 166666666 instructions every second Here is the picture of the CPU with the two new registers added to it There they are under the Control Section connected to the bus The IAR has a set and enable the IR only has a setjust like TMP and MAR because their outputs are not connected to the bus so we never need to turn them off Below is the wiring within the Control Section that does the fetch part of the instruction cycle It uses the first three steps of the stepper and is the same for all types of instructions The steppers first three steps are shown here and result in fetching the next instruction from RAM Then the rest of the steps execute the instruction Exactly what will be done in steps 4 5 and 6 is determined by the contents of the instruction that was fetched Then the stepper starts over fetches the next instruction and executes it The bottom of this diagram includes the Instruction Register Notice that we have given numbers to the individual bits of the IR o at the left through 7 on the right We will be referring to the individual bits soon Here are the details of exactly how steps 1 2 and 3 result in fetching an instruction in our little computer Step 1 is the most complicated because we actually accomplish two things at the same time The main thing we want to do is to get the address in IAR over to MAR This is the address of the next instruction that we want to fetch from RAM If you look at the wire coming out of step 1 of the stepper you can see that two of the places it is connected to are the enable of IAR and the set of MAR Thus the contents of IAR will be placed on the bus during clk e and set into MAR during clk s Sometime during the instruction cycle we need to add 1 to the value in IAR and since IAR is already on the bus we might as well do it now If we dont send anything to the ALUs op bits they will all be zero and since 000 is the code for ADD the ALU will be doing an ADD operation on whatever is on its two inputs and presenting the answer to ACC One input comes from the bus which has IAR on it during this time If we also turn on the bus 1 bit during step 1 the other input to the ALU will be a byte with the binary value of 1 If we turn on the set of ACC during clk swe will capture the sum of IAR plus 1 in ACC This just happens to be the address of the instruction that we will want to fetch after we are done with the current one Step 2 enables the currently selected byte in RAM onto the bus and sets it into IR This is the instruction that we will execute in steps 4 5 and 6 of this instruction cycle In the diagram you can see that the wire coming from step 2 is connected to the enable of RAM and the set of IR In step 3 we need to finish updating IAR We added 1 to it in step 1 but the answer is still in ACC It needs to be moved to IAR before the beginning of the next instruction cycle So you can see the wire coming out of step 3 is connected to enable of ACC and set of IAR By the time we get to step 4 the instruction has already been moved from RAM to IR and now steps 4 5 and 6 can then do whatever is called for by the contents of IR When that operation is done and the stepper is reset the sequence will start over again but now IAR has had 1 added to it so the instruction at the next RAM address will be fetched and executed This idea of putting a series of instructions in RAM and having the CPU execute them is a great invention INSTRUCTIONS We now have this new register called the Instruction Register which contains a byte that is going to tell the Control Section what to do The patterns that are put into this register have a meaning Sounds like another code and indeed it is This code will be called the Instruction Code Since we are building this computer from scratch we get to invent our own instruction code We will take the 256 different codes that can be put in the Instruction Register and decide what they will mean Then we have to design the wiring inside the control unit that will make these instructions do what we said they would do Do you remember the binary number code We said that it was the closest thing to a natural computer code because it was based on the same method we use for our normal number system Then there was the ASCII code which was just invented by a bunch of people at a meeting There is nothing natural about ASCII at all it was just what those people decided it would be Now we have the Instruction Code which will also be a totally invented code nothing natural about it Many different instruction codes have been invented for many different types of computers We will not study any of them here nor will you need to study any of them later unless you are going to go on to a highly technical career where that is necessary But all Instruction Codes are similar in that they are what make the computer work The only Instruction Code in this book will be one that we invent for our simple computer The most important thing in inventing our Instruction Code will be how simple we can make the wiring that will make the code work How many different instructions could there be Since the instruction register is a byte there might be as many as 256 different instructions Fortunately we will only have nine types of instructions and all 256 combinations will fall into one of these categories They are pretty easy to describe All instructions involve moving bytes across the bus The instructions will cause bytes to go to or from RAM to or from registers and sometimes through the ALU In the following chapters for each type of instruction we will look at the bits of that instruction the gates and wiring necessary to make it work and another handy code we can use to make writing programs easier THE ARITHMETIC OR LOGIC INSTRUCTION This first type of instruction is the type that uses the ALU like our ADD operation earlier As you recall the ALU has eight things it can do and for some of those things it uses two bytes of input for other things it only uses one byte of input And in seven of those cases it has one byte of output This type of instruction will choose one of the ALU operations and two registers This is the most versatile instruction that the computer can do It actually has 128 variations since there are eight operations and four registers and you get to choose twice from the four registers That is eight times four times four or 128 possible ways to use this instruction Thus this is not just one instruction but rather it is a whole class of instructions that all use the same wiring to get the job done Here is the Instruction Code for the ALU instruction If the first bit in the Instruction Register is a 1 then this is an ALU instruction Thats the simplicity of it If the first bit is on then the next three bits in the instruction get sent to the ALU to tell it what to do the next two bits choose one of the registers that will be used and the last two bits choose the other register that will be used Therefore the ALU Instruction 1 to add 000 Register 2 10 and Register 3 11 and place the answer in Register 3 would be 1000 1011 If you placed this code 1000 1011 in RAM at address 10 and set the IAR to 10 and started the computer it would fetch the 1000 1011 from address 10 place it in IR and then the wiring in the control section would do the addition of R2 and R3 If you choose a one input operation such as SHL SHR or NOT the byte will come from the Reg A go through the ALU and the answer will be placed in the Reg B You can choose to go from one register to another such as R1 to R3 or choose to go from one register back into the same one such as R2 to R2 When you do the latter the original contents of the register will be replaced For two input operations Reg A and Reg B will be sent to the ALU and the answer will be sent to Reg B So whatever was in Reg B which was one of the inputs to the operation will be replaced by the answer You can also specify the same register for both inputs This can be useful for instance if you want to put all zeros in Register 1 just XOR R1 with R1 No matter what is in R1 to begin with all bit comparisons will be the same which makes the output of all bits zeros which gets placed back into R1 The CMP operation takes two inputs and compares them to see if they are equal and if not if the first one is larger But the CMP operation does not store its output byte It does not replace the contents of either input byte The wiring in the Control unit for the ALU instruction is pretty simple but there is one extra thing that will be used by many types of instructions that we need to look at first This has to do with the registers In Doing Something Useful Revisited we used two registers To use them we just connected the AND gate for each register to the desired step of the stepper This was fine but in the ALU instruction and many others there are bits in the instruction register that specify which register to use Therefore we dont want to wire up directly to any one register we need to be able to connect to any of the registers but let the bits in the instruction choose exactly which one Here is the Control Section wiring that does it Look at the right side first When we want to set a generalpurpose register we connect the proper step to this wire that we will call Reg B As you can see elk s is connected to all four AND gates Reg B is also connected to all four AND gates But these four AND gates each have three inputs The third input to each AND gate comes from a 2x4 decoder You remember that one and only one output of a decoder is on at any given time so only one register will actually be selected to have its set bit turned on The input to the decoder comes from the last two bits of the IR so they determine which one register will be set by this wire labeled Reg B If you look back at the chart of the bits of the ALU Instruction Code it shows that the last two bits of the instruction are what determine which register you want to use for Reg B The left side of the picture is very much like the right side except that there are two of everything Remember that in an ALU instruction such as ADD we need to enable two registers one at a time for the inputs to the ALU The last two bits of the instruction are also used for Reg B on the left and you can see that elk e Reg B and a decoder are used to enable one register during its proper step Bits 4 and 5 of the IR are used to enable Reg A during its proper step using a separate decoder and a wire called Reg A The outputs of these two structures are ORed together before going to the actual register enable bits We will never select Reg A and Reg B at the same time What happens when the instruction that has been fetched begins with a l That means that this is an ALU instruction and we need to do three things First we want to move Reg B to TMP Then we want to tell the ALU which operation to do put Reg A on the bus and set the output of the ALU into ACC Then we want to move ACC to Reg B Bit o of the IR is the one that determines if this is an ALU instruction When Bit o is on the things that Bit o is wired up to make all of the steps of an ALU instruction occur The next diagram shows the eight gates and the wires that are added to the Control Section that make steps 4 5 and 6 of an ALU instruction do what we need them to do In the diagram below just above and to the left of the IR there are three AND gates The outputs of these gates go to the three op wires on the ALU that tell it which operation to do Each of these three AND gates has three inputs One input of each gate is wired to bit o of the IR A second input of each gate is wired to step 5 from the stepper The remaining input of each gate is wired to bits 1 2 and 3 of the IR Therefore the three wires that go to the ALU will be 000 at all times except during step 5 when IR bit o happens to be a 1 At such a time the wires going to the ALU will be the same as bits 1 2 and 3 of the IR IR bit o continues up the diagram turns right and is connected to one side of three more AND gates The other sides of these gates are connected to Steps 4 5 and 6 The output of the first gate comes on during step 4 and you can see it going to two places On the left it enables Reg B onto the bus and on the right it sets the bus into TMP This step is actually not necessary for the SHL SHR and NOT operations but it doesnt harm anything and it would be fairly complicated to get rid of so for simplicitys sake well just leave it this way The second gate comes on during step 5 the same step that the ALU gets its orders and going to the left is a wire that enables Reg A onto the bus The ALU now has one input in TMP the other input on the bus and its operation specified by those three op wires so on the right is a wire that sets the answer into ACC The third gate turns on during step 6 The wire going to the left enables ACC onto the bus and the wire going to the right sets the bus into Reg B There is just one special situation in an ALU instruction and that is when the operation is CMP code 111 For a compare operation we do not want to store any results back into Reg B Therefore there is a three input AND gate connected to IR bits 1 2 and 3 which is then connected to a NOT gate and then to a third input on the AND gate that does step 6 of the ALU instruction So when the operation is 111 the first AND will come on the NOT will go off and the output of the Step 6 AND gate will not turn on This ALU instruction is now done Step 7 resets the stepper which then goes through its steps again fetching the next instruction etc etc We are going to invent one more thing here and that is a shorthand way of writing CPU instructions on a piece of paper In the Instruction Code 1000 1011 means Add R2 to R3 but it takes a lot of practice for a person to look at 1000 1011 and immediately think of addition and registers It also would take a lot of memorization to think of it the other way around that is if you wanted to XOR two registers what is the Instruction Code for XOR It would be easier to write something like ADD R2R3 or XOR R1R1 This idea of using a shorthand has a name and it is called a computer language So along with inventing an instruction code we will also invent a computer language that represents the instruction code The ALU instruction results in the first eight words of our new language When a person wants to write a computer program he can write it directly in the instruction code or use a computer language Of course if you write a program in a computer language it will have to be translated into the actual instruction code before it can be placed in RAM and executed THE LOAD AND STORE INSTRUCTIONS The Load and Store instructions are pretty simple They move a byte between RAM and a register They are very similar to each other so we will cover both of them in one chapter Well get to the details of these instructions in a moment but first we need to have something that tells us when we have a Load or Store instruction in the Instruction Register With the ALU instruction all we needed to know was that bit o was on The code for every other type of instruction begins with bit o off so if we connect a NOT gate to bit o when that NOT gate turns on that tells us that we have some other type of instruction In this computer there are eight types of instructions that are not ALU instructions so when bit o is off we will use the next three bits of the IR to tell us exactly which type of instruction we have The three bits that went to the ALU in an ALU instruction also go to a 3x8 decoder here in the Control Section As you remember one and only one of the outputs of a decoder is on at all times so we will have AND gates on the outputs to prevent any output from going anywhere during an ALU instruction But when it is not an ALU instruction the one output of the decoder that is on will get through its AND gate and in turn will be connected to some more gates that make the appropriate instruction work In the diagram below you can see IR bits 1 2 and 3 going into a decoder which has eight AND gates on its outputs IR bit o has a NOT gate which goes to the other side of those eight AND gates This decoder is used for the rest of the instructions that our computer will have This chapter is about the instructions that use the first two outputs of the decoder the ones that come on when the IR starts with 0000 or 0001 The first instruction moves a byte from RAM to a register this is called the Load instruction The other one does the same in reverse it moves a byte from a register to RAM and is called the Store instruction The Instruction Code for the Load instruction is 0000 and for the Store instruction is 0001 The remaining four bits in both cases specify two registers just like the ALU instruction did but in this case one register will be used to select one of the locations in RAM and the other register will either be loaded from or stored to that RAM location Step 4 is the same for both instructions One of the registers is selected by IR bits 4 and 5 and is enabled onto bus The bus is then set into MAR thus selecting one address in RAM In step five IR bits 6 and 7 select another one of the CPU registers For the Load instruction RAM is enabled onto the bus and the bus is set into the selected register For the Store instruction the selected register is enabled onto the bus and the bus is set into RAM Each of these instructions only need two steps to complete step 6 will do nothing Here are two new words for our computer language Language Meaning LD RARB Load RB from RAM address in RA ST RARB Store RB to RAM address in RA THE DATA INSTRUCTION Now here is an interesting instruction All it does is load a byte from RAM into a Register like the Load instruction above The thing that is different about it though is where in RAM it will get that byte In the Data instruction the data comes from where the next instruction ought to be So you could consider that this instruction is actually two bytes long The first byte is the instruction and the next byte is some data that will be placed into a register This data is easy to find because by the time we have the instruction in the IR the IAR has already been updated and so it points right to this byte Here is the Instruction Code for the Data instruction Bits o to 3 are 0010 Bits 4 and 5 are not used Bits 6 and 7 select the register that will be loaded with the data that is in the second byte All this instruction needs to do is in step 4 send IAR to MAR and in step 5 send RAM to the desired CPU register However there is one more thing that needs to happen Since the second byte of the instruction is just data that could be anything we do not want to execute this second byte as an instruction We need to add 1 to the IAR a second time so that it will skip this byte and point to the next instruction We will do this the same way that it is done in steps 1 and 3 In step 4 when we send IAR to MAR we will take advantage of the fact that the ALU is calculating IAR plus something at the same time we will turn on the Bus 1 and set the answer into ACC Step 5 still moves the data to a Register and in step 6 we can move ACC to IAR Here is another new word for our computer language THE SECOND GREAT INVENTION The first great invention is this idea of having a string of instructions in RAM that get executed one by one by the CPU But our clock is very fast and the amount of RAM we have is limited What will happen in far less than a second when we have executed every instruction in RAM Fortunately we will not have to answer that question because someone came up with another type of instruction that is so important that it qualifies as the second great invention necessary to allow the computer to do what it does Because of the versatile arrangement of our CPU and its Control Section it is an extremely simple thing to make this work but its importance should not be lost because of this simplicity This new type of instruction is called a Jump instruction and all it does is to change the contents of the IAR thus changing where in RAM the next and subsequent instructions will come from The exact type of Jump instruction described in this chapter is called a Jump Register instruction It simply moves the contents of Reg B into the IAR Here is the Instruction Code for it The computer is executing a series of instructions in RAM one after the other and suddenly one of those instructions changes the contents of the IAR What will happen then The next instruction that will be fetched will not be the one that follows the last one It will be the one that is at whatever RAM address was loaded into the IAR And it will carry on from that point with the next one etc until it executes another jump instruction The wiring for the Jump Register instruction only needs one step In step 4 the selected register is enabled onto the bus and set into the IAR and that is all If we wanted to speed up our CPU we could use step 5 to reset the stepper But to keep our diagram simple we wont bother with that Steps 5 an 6 will do nothing Here is another new word for our computer language ANOTHER WAY TO JUMP This is another type of Jump instruction It is similar to the Data instruction in that it uses two bytes It replaces the IAR with the byte that is in RAM immediately following the instruction byte thus changing where in RAM the next and subsequent instructions will come from Here is the Instruction Code for it Bits 4 5 6 and 7 are not used in this instruction This exact type of Jump instruction is just called a Jump It is useful when you know the address that you are going to want to jump to when you are writing the program The Jump Register Instruction is more useful when the address you are going to want to jump to is calculated as the program in running and may not always be the same One of the things you can do with a Jump instruction is to create a loop of instructions that execute over and over again You can have a series of fifty instructions in RAM and the last instruction Jumps back to the first one Like the Data instruction the IAR already points to the byte we need Unlike the Data Instruction we dont need to add 1 to the IAR a second time because we are going to replace it anyway So we only need two steps In step 4 we send IAR to MAR In step 5 we move the selected RAM byte to the IAR Step 6 will do nothing Here is the wiring that makes it work Here is another new word for our computer language THE THIRD GREAT INVENTION Here is the third and last invention that makes a computer a computer This is just like the Jump Instruction but sometimes it jumps and sometimes it doesnt Of course to jump or not to jump is just two possibilities so it only takes one bit to determine which will happen Mostly what we are going to introduce in this chapter is where that one bit comes from Do you remember the Carry bit that comes out of and goes back into the ALU This bit comes either from the adder or from one of the shifters If you add two numbers that result in an amount that is greater than 255 the carry bit will come on If you left shift a byte that has the left bit on or right shift a byte that has the right bit on these situations will also turn on the ALUs carry out bit There is also a bit that tells us if the two inputs to the ALU are equal another one that tells us if the A input is larger and one more bit that tells us if the output of the ALU is all zeros These bits are the only things that we have not yet found a home for in the CPU These four bits will be called the Flag bits and they will be used to make the decision for a Jump If instruction as to whether it will execute the next instruction in RAM or jump to some other address What we are trying to get the computer to be able to accomplish is for it to first execute an ALU instruction and then have one or more Jump If instructions following it The Jump If will jump or not depending on something that happened during the ALU instruction Of course by the time the Jump If is executing the results of the ALU instruction are long gone If you go back and look at the details of the ALU instruction it is only during step 5 that all of the proper inputs are going into the ALU and the desired answer is coming out It is at this time that the answer is set into ACC The timing is the same for all four Flag bits they are only valid during step 5 of the ALU instruction Therefore we need a way to save the state of the Flag bits as they were during step 5 of the ALU instruction Here is the last register that we are going to add to the CPU This will be called the FLAG register and we are only going to use four bits of it one for each of the flags The Flag bits from the ALU are connected to the input of this register and it will be set during step 5 of the ALU instruction just like ACC and it will stay set that way until the next time an ALU instruction is executed Thus if you have an ALU instruction followed by a Jump If instruction the Flag bits can be used to decide whether to Jump or not Every instruction cycle uses the ALU in step 1 to add 1 to the address for the next instruction but only step 5 of the ALU instruction has a connection that sets the Flags We did not show this connection in the wiring for the ALU instruction because we had not yet introduced the Flag Reg but it will appear in the completed Control Section diagram This combination of Flag bits and the Jump IF instruction is the third and last great invention that makes computers as we know them today work Here is the Instruction Code for a Jump If instruction The second four bits of the instruction tell the CPU which flag or flags should be checked You put a 1 in the instruction bits corresponding to the flags that you want to test for If any one of the Flags that you test is on the jump will happen This arrangement gives us a number of ways to decide whether to jump or not There is a second byte that contains the address to jump to if the jump is taken Here is the wiring in the Control Section that makes the Jump If instruction work Step 4 moves IAR to MAR so we are prepared to get the Jump to Address that we will use IF we jump But because we might not jump we also need to calculate the address of the next instruction in RAM And so step 4 also turns on Bus 1 and sets the answer in ACC In step 5 we move ACC to IAR so we are ready to fetch the next instruction IF we dont jump Step 6 is where the decision is made We will move the second byte of the instruction from RAM to IAR IF the third input to that AND gate is on That third input comes from an OR gate with four inputs Those four inputs come from the four Flag bits after being ANDed with the last four bits of the Jump If instruction in IR If for instance there is a 1 in the Equal bit of the instruction and the Equal Flag bit is on then the jump will occur Here are more words for our computer language J means Jump C means Carry A means A is larger E means A Equals B and Z means that the answer is all Zeros Here are the words of the language that test a single Flag You can also test more than one flag bit at the same time by putting a 1 in more than one of the four bits Actually since there are four bits there are 16 possible combinations but the one with all four bits off is not useful because it will never jump For the sake of completeness here are the rest of the possibilities JCAE Addr Jump if Carry or A larger or Equal to B JCAZ Addr Jump if Carry or A larger or Zero JCEZ Addr Jump if Carry or A Equals B or Zero JAEZ Addr Jump if A larger or Equal to B or Zero JCAEZ Addr Jump if Carry A larger Equal or Zero THE CLEAR FLAGS INSTRUCTION There is one annoying detail that we need to have here When you do addition or shifting you have the possibility of getting the carry flag turned on by the operation This is necessary we use it for the Jump If instruction as in the previous chapter The Carry Flag is also used as an input to the addition and shift operations The purpose of this is so you can add numbers larger than 255 and shift bits from one register to another The problem that arises is that if you are just adding two singlebyte numbers you dont care about any previous Carry but the Carry Flag may still be set from a previous operation In that case you might add 22 and get 5 Bigger computers have several ways to do this but for us we will just have a Clear Flags Instruction that you need to use before any adds or shifts where an unexpected carry bit would be a problem Here is the Instruction Code for this instruction Bits 4 5 6 and 7 are not used The wiring for this is very simple and a bit tricky We will not enable anything onto the bus thus it and the A ALU input will be all zeros We will turn on Bus 1 so the B input is 0000 0001 We wont send an operation to the ALU so it will be in ADD mode The ALU therefore will be adding 0 and 1 and there may be a carry input The answer then will be either 0000 0001 or 0000 0010 But there will be no carry output the answer is not zero and B is larger than A so equal and A larger will both be off We set the Flag Reg at this time while all four Flag bits are off Here is another word for our language TA DAA We have now wired up the Control Section of our CPU As a result we can place a series of instructions in RAM and the Clock Stepper Instruction Register and wiring will fetch and execute those instructions Here is the entire control section Yes this looks pretty complicated but we have looked at every part of it already The only thing we had to add were some OR gates because most of the enables and sets need multiple connections This actually has a lot fewer parts than the RAM but that was much more repetitive Most of the mess here is just getting the wires from one place to another The byte that is placed in the Instruction Register causes a certain activity to occur Each possible pattern causes a different activity Therefore we have a code where each of the 256 possible codes represents a different specific activity As mentioned this is called the Instruction Code Another name for it is machine language because this is the only language code that the machine computer understands You tell the machine what to do by giving it a list of orders you want it to carry out But you have to speak the only language that it understands If you feed it the right bytesized patterns of ons and offs you can make it do something that will be useful Here are all of the Instruction Codes and our shorthand language brought together in one place Believe it or not everything you have ever seen a computer do is simply the result of a CPU executing a long series of instructions such as the ones above A FEW MORE WORDS ON ARITHMETIC We dont want to spend a lot of time on this subject but the only thing that we have seen so far that looks like arithmetic is the adder so we will look at simple examples of slightly more complex arithmetic Not to teach you how to act like a computer but just to prove to you that it works Here is how you do subtraction It is done with the adder and the NOT gates If you want to subtract R1 from R0 first you NOT R1 back into itself Then you add 1 to R1 then you Add R0 to R1 This shows an example of subtracting 21 from 37 The last step is adding 37 235 the answer of which should be 272 But a single register cannot hold a number larger than 255 Therefore the adder turns on its Carry bit and the eight bits remaining of the answer are 0001 0000 which is 16 the correct answer for 37 minus 21 Why does NOTting and ADDing result in subtraction Why do you have to add 1 after NOTting Why do you ignore the carry bit We are not going to attempt to answer any of these questions in this book These are the details that keep a very few engineers from getting a good nights sleep These brave people study these problems and design ways for ordinary people to not have to understand it Here is how you do multiplication When we do multiplication with a pencil and paper in the decimal system you have to remember your multiplication tables you know 3 times 8 equals 24 6 times 9 equals 54 etc In binary multiplication is actually much easier than in decimal 1 times 1 equals 1 and for every other combination the answer is o It just couldnt get much simpler than that Heres an example of multiplying 5 times 5 with pencil and paper in binary If you look at whats happening here if the right digit of the bottom number is a 1 you put the top number in the answer Then for every digit to the left of that shift the top number left and if the bottom digit is a 1 add the shifted top number to the answer When you get through the eight bits of the bottom number youre done So multiplication is accomplished with the adder and the shifters Its as simple as that You can write a simple program like this R0 contains the bottom number R1 contains the top number and R2 will contain the answer R3 is used to jump out of the loop after going through it eight times See what happens with the Registers as this program goes through its loop the first three times The important thing that has happened here is that R1 has been added to R2 twice It happened on the first time through when R1 contained 0000 0101 and on the third time through after R1 had been shifted left twice and therefore contained 0001 0100 R2 now contains 00011001 binary which is 1681 or 25 decimal which is the correct answer for 5 times 5 The loop will repeat 5 more times until the bit in R3 gets shifted out to the Carry Flag but the total wont increase because there are no more is in R0 This program will go through eight times We start with 0000 0001 in R3 Near the end of the program R3 gets shifted left The first seven times through there will be no carry so the program will get to the JMP 53 and go back up to the third instruction of the program The eighth time R3 gets shifted left the one bit that is on gets shifted out of R3 and into the Carry flag Therefore the JC 68 will jump over the JMP 53 and carry on with whatever instructions come after this The byte in R0 gets shifted right to test which bits are on The byte in R1 gets shifted left to multiply it by two When there was a bit in R0 you add R1 to R2 And thats all there is to it One thing we do not address in this example is what happens if the answer of the multiplication is more than 255 If a multiplication program multiplies two onebyte numbers it ought to be able to handle a twobyte answer That would take care of any two numbers that you might start with This would be accomplished with the carry flag and some more Jump If instructions We wont torture the reader with the details Reading a program like the one above is an entirely different skill than reading the diagrams and graphs we have seen so far in the book I hope you were able to follow it but no one is expected to become an expert at reading programs because of this book Division also can be done by our computer There are several ways it can be done and we are not going to examine any of them in any detail Just imagine the following simple method Lets say you want to divide fifteen by three If you repeatedly subtract three from fifteen and count the number of subtractions you can accomplish before the fifteen is all gone that count will be the answer Like these five steps 115312 21239 3936 4633 5330 This is easily turned into a program Computers also have ways of handling negative numbers and numbers with decimal points The details are very tedious and studying them would not enhance our understanding of how computers work It still comes down to nothing more than NAND gates Our simple computer could do all of these things with programs THE OUTSIDE WORLD What we have described so far is the whole computer It has two parts the RAM and the CPU Thats all there is These simple operations are the most complicated things that a computer can do The ability to execute instructions modify bytes with the ALU the ability to jump from one part of the program to another and most importantly the ability to jump or not jump based on the result of a calculation This is what a computer is able to do These are simple things but since it operates so quickly it can do huge numbers of these operations that can result in something that looks impressive These two parts make it a computer but if all the computer could do is run a program and rearrange bytes in RAM no one would ever know what it was doing So there is one more thing that the computer needs in order to be useful and that is a way to communicate with the outside world Dealing with anything outside of the computer is called InputOutput or IO for short Output means data going out of the computer Input means data coming into the computer Some things are input only such as a keyboard some things are output only like a display screen some things do both input and output like a disk All we need for IO is a few wires and a new instruction For the wires all we are going to do is to extend the CPU bus outside of the computer and add four more wires to go with it This combination of 12 wires will be called the IO Bus Everything that is connected to the computer is attached to this one IO bus The devices that are connected to the IO bus are called peripherals because they are not inside the computer they are outside of the computer on its periphery the area around it More than one thing can be attached to the IO bus but the computer controls the process and only one of these things is active at a time Each thing attached to the IO bus has to have its own unique IO address This is not the same as the addresses of the bytes in RAM it is just some number that the peripheral will recognize when placed on the bus Here is what the IO bus looks like in the CPU there at the bottom right of the drawing In the diagram below are the wires of the IO Bus The CPU Bus is the same eightwire bundle that goes everywhere else The InputOutput wire determines which direction data will be moving on the CPU bus either in or out The DataAddress wire tells us whether we will be transferring a byte of data or an IO Address that selects one of the many devices that could be attached to the IO bus IO Clk e and IO Clk s are used to enable and set registers so that bytes can be moved back and forth Here is the control section wiring for the new instruction that controls the IO bus This shows where the four new wires for the IO bus come from They are at the bottom right of the drawing They were also shown on the full control section diagram a few chapters back Sorry if that was confusing but having that diagram in the book once was enough IR bits 4 and 5 are placed on the IO bus at all times To make the IO operation happen only one step is needed For Output Reg B is enabled and IO Clk s is turned on and off during step 4 Steps 5 and 6 do nothing For Input IO Clk e is enabled and Reg B is set during step 5 Steps 4 and 6 do nothing Here is the Instruction Code for the IO instruction This one instruction can be used in four different ways depending on IR bits 4 and 5 and therefore there are four new words for our language Each IO device has its own unique characteristics and therefore needs unique parts and wiring to connect it to the IO bus The collection of parts that connects the device to the bus is called a device adapter Each type of adapter has a specific name such as the keyboard adapter or the disk adapter The adapter does nothing unless its address appears on the bus When it does then the adapter will respond to the commands that the computer sends to it With an OUT Addr instruction the computer turns on the address wire and puts the address of the device it wants to talk to on the CPU bus The peripheral recognizes its address and comes to life Every other peripheral has some other address so they wont respond We are not going to describe every gate in the IO system By this time you should believe that bytes of information can be transferred over a bus with a few control wires The message of this chapter is only the simplicity of the IO system The CPU and the RAM are the computer Everything else disks printers keyboards the mouse the display screen the things that make sound the things that connect to the internet all these things are peripherals and all they are capable of doing is accepting bytes of data from the computer or sending bytes of data to the computer The adapters for different devices have different capabilities different numbers of registers and different requirements as far as what the program running in the CPU must do to operate the device properly But they dont do anything fancier than that The computer controls the process with a very few simple IO commands that are executed by the CPU THE KEYBOARD A keyboard is one of the simplest peripherals connected to the IO bus It is an input only device and just presents one byte at a time to the CPU The keyboard has eight wires inside its own little bus as shown on the right When you press a key it simply connects electricity to the wires necessary to create the ASCII code corresponding to the key that was pressed That little box that says Control is also notified when a key is pressed and sets the ASCII code into the Keycode Register After pressing a key there will be an ASCII code waiting in the Keycode Register Heres how the CPU gets that code into one of its registers AND gate 1 has eight inputs They are connected to the CPU bus four of them through NOT gates Thus this AND gate will turn on any time the bus contains 0000 1111 This is the IO address of this keyboard adapter AND gate 2 comes on only during clk s time of an OUT Addr instruction It operates the set input of a Memory bit If the bus contains 0000 1111 at this time the i input will be on and the Memory bit will turn on When this Memory bit is on it means that the keyboard adapter is active AND gate 3 comes on during elk e time of an IN Data instruction If the Memory bit is on AND gate 4 will come on and the Keycode Register will be enabled onto the bus which will be set into Reg B in the CPU Every adapter that is connected to the IO bus needs to have the type of circuitry we see in gates 1 and 2 and the memory bit above Each adapter will have a different combination that turns gate 1 on this is what allows the CPU to select each adapter individually Here is a little program that moves the current keypress into Reg 3 in the CPU That little Control box clears the Keycode Register after it has been sent to the CPU The program running in the CPU will check the keyboard adapter on a regular basis and if the byte that it receives is all zeros then no key has been pressed If the byte has one or more bits on then the program will do whatever the program has been designed to do with a keystroke at that time Again we are not going to go through every gate in the Keyboard adapter All device adapters have the same sorts of circuitry in order to be able to respond when they are addressed and send or receive bytes of information as needed But it is no more complicated than that That is all that IO devices and adapters do THE DISPLAY SCREEN Television and computer display screens work the same way the main difference between them is only what they display This is not actually computer technology because you dont need a display screen to have a computer but most computers do have a screen and the computer spends a lot of its time making the screen look like something so we need to know a little bit about how it works Television appears to give you moving pictures with sound The pictures and sound are done separately and in this chapter we are only concerned with how the picture works The first thing to know is that although the picture appears to be moving it is actually a series of still pictures presented so quickly that the eye doesnt notice it You probably already knew that but heres the next thing You have seen motion picture film It is a series of pictures To watch a movie you put the film in a projector which shines light through one picture then moves the film to the next picture shines light through it etc It usually runs at 24 pictures per second which is fast enough to give the illusion of a constantly moving picture Television goes a bit faster about 30 pictures per second but there is another much bigger difference between film and television With the movie film each still picture is shown all at once Each picture is complete when you shine the light through it every part of the picture appears on the screen simultaneously Television is not capable of doing this It does not have a whole picture to put on the screen all at once All that a television can do at one instant in time is to light up one single dot on the screen It lights up one dot then another dot then another very quickly until one whole pictures worth of dots has been lit This whole screens worth of dots makes up one still picture thus it has to light up all of the dots within one thirtieth of a second and then do it all over again with the next picture etc until it has placed 30 pictures worth of dots on the screen in one second So the TV is very busy lighting up individual dots 30 times the number of dots on the screen every second Usually the top left dot is lit first then the one to its right and so on across the top of the screen to the top right corner Then it starts with the second line of dots going across the screen again the third line etc until it has scanned the entire screen The brightness of each dot is high or low so that each part on the screen gets lit up to the proper brightness to make the screen look like the intended image At any one instant in time the television is only dealing with one single solitary dot on the screen So with television there are two illusions the illusion of motion coming from a series of still pictures as well as the illusion of complete still pictures that are actually drawn one dot at a time This second illusion is aided by what the screen in made of each dot only gets lit up for a tiny fraction of a second and it starts to fade away immediately Fortunately whatever the screen is made of that glows continues to glow to some degree between one time when the dot is lit up and 130th of a second later when that same dot gets lit up again To the eye you just see a moving picture but there are a lot of things going on to make it appear that way In a computer a single dot on the screen is called a picture element or pixel for short Computer screens work just like televisions They also have to scan the entire screen 30 times a second to light up each individual pixel and thereby make an image appear Even if the content of the screen is not changing something in the computer has to scan that unchanging image onto the screen 30 times every second No scanning no picture thats just the way it works Were not going to go into the same amount of detail here that we did with the CPU and the RAM those two are what make it a computer but if we want to know how our computer is able to put something on the screen that we can read we need to have the basic idea of how it works In this chapter we will look at the simplest kind of screen the kind that is black and white and whose pixels can only either be fully on or fully off This type of screen can display characters and the type of pictures that are made of line drawings Later in the book we will see the few simple changes that enable a screen to display things like color photographs The major parts are three First there is the computer we have seen how that works It has an IO Bus that can move bytes to and from things outside of the computer Second is the screen The screen is just a large grid of pixels each of which can be selected one at a time and while selected can either be turned on or not The third item is the display adapter The display adapter is connected to the IO Bus on one side and to the screen on the other side The heart of a display adapter is some RAM The display adapter needs its own RAM so it can remember which pixels should be on and which pixels should be off In the type of screen we are going to describe here there needs to be one bit in RAM for each pixel on the screen In order to make the screen scan every pixel 30 times every second the Display Adapter needs its own clock that ticks at a speed that is 30 times the number of pixels on the screen At each tick of the clock one pixel is selected and it is turned on or not by the corresponding bit from the RAM As an example lets use an old type of screen It is a black and white screen that displays 320 pixels across the screen and 200 pixels down That comes out to 64000 individual pixels on the screen Each pixel on the screen has a unique address consisting of two numbers the first being the leftright or horizontal position and the other being the updown or vertical position The address of the top left pixel is 00 and the bottom right pixel is 319199 64000 pixels times 30 pictures per second means that this Display Adapters clock needs to tick 1920000 times per second And since there are eight bits in a byte we will need 8000 bytes of display RAM to tell each of the 64000 screen pixels whether to be on or off The display adapter has a register that sets the horizontal position of the current pixel The display adapter adds 1 to this register at every tick of the clock It starts at zero and when the number in it gets to 319 the next step resets it back to zero So it goes from zero to 319 over and over again There is also a register that sets the vertical position of the current pixel Every time the horizontal register gets reset to zero the display adapter adds 1 to the vertical register When the vertical register reaches 199 the next step will reset it to zero So as the horizontal register goes from zero to 319 200 times the vertical register goes from zero to 199 once The currently selected screen pixel is controlled by these registers so as the horizontal register goes from o to 319 the current pixel goes across the screen once Then the vertical register has one added to it and the current pixel moves down to the first pixel on the next line Thus the clock and the horizontal and vertical registers select each pixel on the screen one at a time going left to right in one row then selecting each pixel in the next row down then the next etc until every pixel on the screen has been selected one time Then it starts all over again At the same time there is another register that contains a display RAM address This register also gets stepped through although we only need one new byte for every eight pixels The bits of each byte one at a time are sent to the screen at eight consecutive pixels to turn them on or off After every eight pixels the RAM address register has 1 added to it By the time all of the pixels have been stepped through the entire RAM has also been stepped through and one entire picture has been drawn When the horizontal and vertical registers have both reached their maximums and are reset to zero the RAM address is also reset to zero The display adapter spends most of its time painting the screen The only other thing it has to do is to accept commands from the IO Bus that will change the contents of the display adapter RAM When the program running in the CPU needs to change whats on the screen it will use the IO OUT command to select the display adapter and then send a display adapter RAM address and then a byte of data to store at that address Then as the adapter continues to repaint the screen the new data will appear on the screen at the appropriate spot The display adapter RAM is built differently than the RAM in our computer It keeps the input and output functions separate The inputs of all storage locations are connected to the input bus and the outputs of all storage locations are connected to the output bus but the input bus and the output bus are kept separate Then there are two separate memory address registers one for input and one for output The input MAR has a grid that only selects which byte will be set and the output MAR has a separate grid that only selects which byte will be enabled With this setup the screen and the display RAM can both be continuously scanned using only the output MAR and the enable bit When the IO Bus is used to write into the display RAM it uses only the input MAR and the set bit This is how the display adapter creates an image on the screen Because of the way it works there is an interesting relationship between which bits in the display RAM correspond to which pixels on the screen As it scans the first eight pixels of the top line it uses the individual bits of byte o of its RAM to turn the pixels on or off As it scans the second eight pixels it uses the individual bits of byte 1 of its RAM etc It takes 40 bytes of RAM to draw the first line and so the last eight pixels which are numbered 312 through 319 come from RAM byte 39 The second row uses byte 40 to draw its first 8 pixels etc If you want to write letters and numbers on the screen how do you do it If you put the ASCII code for A into a byte in the display RAM you will just get eight pixels in a row where one is off then one is on then five are off and the last one is on Thats not what an A should look like There is a solution for this and it involves ANOTHER CODE When you want to print or display written language you need to translate the ASCII code into something that is readable by a live person We have a code 0100 0101 that appears on the ASCII code table next to the letter E But how does the computer turn 0100 0101 into a readable E We have a display screen but the screen is a just a grid of pixels there are no human readable Es in anything we have described so far In order to get an E on the screen there has to be something that makes that shape that we recognize as a letter of the alphabet Therefore we need another code This code is really about little pictures made out of dots For each character that we want to be able to draw on the screen we need a little picture of that character If you take a grid 8 pixels wide and 8 pixels high you could decide which pixels had to be on to make a little picture that looks like the character that you want to draw on the screen like this If you turn this picture into ons and offs you could store it in eight bytes If there are 100 different characters that you want to be able to display on the screen then youd need 100 different little pictures like this and it would require 800 bytes of RAM to store it Our little computer only has a 256 byte RAM so this would be a good time to imagine that larger version that we described earlier These 800 bytes are a type of code known as a font If you want to make a character appear in a certain place on the screen you need to choose the correct little picture from the font and then use IO instructions to copy the eight bytes of the picture to the proper bytes in the display adapters RAM If the pictures in our font are arranged in the same order as the ASCII code table then we can use the numeric value of an ASCII code to find the corresponding picture within the font The ASCII code for E is 0100 0101 If you apply the binary number code to the same pattern of ones and zeros you get the decimal number 69 E then is the 69th code in ASCII and the picture of an E will be the 69th picture within the font Since there are eight bytes in each picture you multiply the 69 by 8 and that tells you that the picture for E will be the eight bytes starting at address 552 Now we need to know where to copy these bytes to in the display RAM Lets say that we want to display an E at the very top left of the screen Where are the bits that turn on the pixels that we are interested in Well the first line is easy it is the first eight bits of the display RAM Address o So we use a series of OUT instructions to copy RAM address 552 to display RAM address o Now where is the second line in the display RAM The display paints all 320 bits of the top row before it moves down to the second row That means that it uses 40 bytes on each row so the top row uses bytes 039 That means that the second byte of the picture of E at RAM address 553 needs to be written at address 40 in the display RAM Similarly the third through eighth bytes get written at bytes 80 120 160 200 240 and 280 When you have done all of that you would then see a complete E on the screen If you wanted to write an X on the screen right next to the E you would locate the eight bytes in the font for X and copy them into display RAM bytes 1 41 81 121 161 201 241 and 281 If you need 27 Es on your screen you just copy the one E in your font to 27 different places in the display RAM Of course this seems like a lot of work just to make a single letter appear on the screen The program that does this would need a loop of instructions that calculates the first from and to addresses then issues the appropriate OUT instructions to copy the first byte to the display RAM Then the loop would repeat updating both addresses each time until all eight bytes had been copied to the appropriate places Were not going to write this program but it could easily be a 50 instruction program that has to loop around eight times before its finished That means that it could take 400 instruction cycles just to put one character on the screen If you drew 1000 characters on the screen that might take 400000 instruction cycles On the other hand thats still only about one quarter of one percent of what this computer can do in one second This just goes to show you why computers need to be so fast The individual things that they do are so small that it takes a huge number of steps to get anything done at all THE FINAL WORD ON CODES We have seen several codes used in our computer Each one was designed for a specific purpose Individual coded messages are put in bytes and moved around and used to get things done The bytes do not know which code was used to choose the pattern that they contain There is nothing in the byte itself that tells you which code it is supposed to be Certain parts of the computer are built with various codes in mind In the ALU the adder and comparator are built to treat bytes as though they contain values encoded with the binary number code So are the Memory Address Register and the Instruction Address Register The Instruction Register is built to treat its contents as though it contains values encoded with the Instruction Code The Display adapter RAM bits are just ons or offs for individual pixels Pictures and fonts are strings of bytes that will result in something that can be recognized by a person when it is organized and the brightnesses are set by the wiring of a display adapter and screen The ASCII code table does not appear anywhere inside the computer because there is no way to represent a letter of the alphabet except by using a code The only places where ASCII gets converted between characters and the code for the character are in the peripherals When you press E on the keyboard you get the ASCII code for an E When you send the ASCII code for an E to a printer it prints the letter E The people who build these peripherals have an ASCII code table in front of them and when they build a keyboard the switch under the fourth button in the second row which has the letter E printed on it is wired up to the proper bus wires to produce the code that appears next to the letter E on the ASCII code table An E is the fifth letter of an alphabet used by people to represent sounds and words in the process of writing down their spoken language The only Es in the computer are the one on the keyboard and the ones that appear on the screen All the Es that are in bytes are just the code that appears next to the E on an ASCII code table They are not Es there is no way to put an E in a computer Even if you put a picture of an E in a computer it isnt actually an E until it is displayed on the screen Thats when a person can look at it and say Thats an E Bytes are dumb They just contain patterns of ons and offs If a byte contains 0100 0101 and you send it to the printer it will print the letter E If you send it to the Instruction Register the computer will execute a Jump instruction If you send it to the Memory Address Register it will select byte number 69 of the RAM If you send it to one side of the Adder it will add 69 to whatever is on the other side of the Adder If you send it to the display screen it will set three pixels on and five pixels off Each of these pieces of the computer is designed with a code in mind but once it is built the mind is gone and even the code is gone It just does what it was designed to do There is no limit to the codes that can be invented and used in a computer Programmers invent new codes all the time Like the cash register in the fast food restaurant mentioned earlier somewhere in that machine is a bit that means include French fries THE DISK Most computers have a disk This is simply another peripheral that is attached to the IO bus The disks mission is very simple it can do two things You can send it bytes which it will store or you can tell it to send back some bytes which were stored previously There are two reasons that most computers have a disk First they have the ability to store a huge number of bytes many times greater than the Computers RAM The CPU can only execute programs that are in RAM it can only manipulate bytes that are in RAM But there is never enough RAM to store all of the things that you may want to do with your computer And so a disk will hold everything and when you want to do one thing the bytes on the disk for that one thing will be copied into RAM and used Then when you want to do something different the bytes for the new activity will be copied from the disk into the same area of RAM that had been used for the first activity The second reason that computers have disks is that the bytes stored on the disk do not disappear when you turn the power off The RAM loses its settings when you turn the computer off when you turn it back on all bytes are 0000 0000 but the disk retains everything that has been written on it A computer bit has been defined so far as a place where there is or is not some electricity But prior to that we defined it as a place that can be in one of two different states On a disk the electric bits are transformed into places on the surface of the disk that have been magnetized one way or the other Since magnets have north and south poles the spot on the disk can be magnetized either northsouth or southnorth One direction would represent a zero and the other direction a one Once a spot is magnetized it stays that way unless the same spot gets magnetized the other way Turning the power off has no effect on the magnetized spots A disk as its name implies is a round thing that spins around quickly It is coated with a material that can be magnetized easily Do you remember the telegraph At the receiving end there is a piece of metal with a wire wrapped around it That piece of metal turns into a magnet when electricity moves through the wire The disk has a tiny version of this called a head mounted on an arm The arm holds the head very close to the surface of the spinning disk and the arm can swing back and forth so that the head can reach any point on the surface of the disk If you put electricity through the head it can magnetize the surface of the disk Also it works the other way around when the head passes over a magnetized area it makes electricity appear in the wires wrapped around the head Thus the head can either write on the disk or read what has been previously written on the disk The bits of the bytes are written one after another on the disk surface The surface of the disk is divided into a series of rings called tracks very close to each other The head can move across the surface and stop on any one of the tracks Each circular track is usually divided into short pieces called sectors Since a disk has two sides usually both sides are coated with the magnetic material and there is a head on each side In RAM every byte has its own address On a disk there is also a way to locate bytes but it is very different You have to specify which head which track and which sector at which a block of bytes is located That is the type of address that the data on a disk has like Head 0 Track 57 Sector 15 And at that address there is not just one byte but a block of bytes typically several thousand For the examples in our book since our RAM is so small we will talk about a disk that stores blocks of 100 bytes When a disk is read or written there is no way to access an individual byte in the block of bytes The whole block has to be transferred to RAM worked on in RAM and then the whole block has to be written back to the disk The disk spins quickly faster than that fan on your desk many popular disks spin 7200 times a minute which is 120 times per second Thats pretty fast but compared to the CPU it is still pretty slow In the time that the disk spins around one time the Clock will tick over eight million times and our CPU will execute well over a million instructions The disk like every peripheral is connected to its own adapter which in turn is connected to the IO bus The disk adapter does a few things It accepts commands to select a head select a track and select a sector It accepts commands to read from or write to the block of bytes at the currently selected head track and sector There will also probably be a command where the CPU can check the current position of the arm and the disk The command to select a head can be completed immediately but when it gets a command to select a track it has to move the head to that track which takes a long time in terms of instruction cycles When it gets a command to select a sector it has to wait for that sector to spin around to where the head is which also takes a long time in terms of instruction cycles When the CPU has determined that the head has arrived at the desired track and sector then the IO commands for reading or writing can be executed and one byte at a time will be transferred over the IO bus A program that reads or writes a block of bytes has to continue the process until the whole block of bytes is complete With our simple IO system the individual bytes move between the disk and a CPU register The program that is running has to move these bytes to or from RAM usually in consecutive locations This is all that a disk does You have probably used a computer that had a disk and didnt need to know anything about heads tracks and sectors And that is a good thing because it is pretty annoying to have to deal with a disk at that level of detail We will look at how a disk is normally used later in the book Another language note There are several words that mean virtually the same thing but for some reason certain words go with certain technologies If you want to send someone a letter first you write it on a piece of paper then when the recipient gets the letter he reads it In the days of tape recorders you would start with a blank tape Then you would record some music on the tape When you wanted to hear the music again you would play the tape When it comes to computer disks putting something on the disk is called writing Getting something off the disk is called reading Putting something into RAM is called writing or storing Getting something out of RAM is called reading or retrieving Putting something into a CPU register is usually called loading Putting music on a disk is sometimes called recording sometimes burning Listening to a disk is still usually called playing but if you are copying it onto your computer then it is called ripping Writing recording storing loading and burning all mean pretty much the same thing Reading retrieving playing and ripping are also very similar They mean the same things its just a difference of words EXCUSE ME MAAM There is one other thing that most computers have as part of their InputOutput system A computer doesnt need one of these to be called a computer so we will not go through every gate needed to build it But it is a very common thing so we will describe how it works You know if Mom is in the kitchen stirring a pot of soup and little Joey comes running in and says I want a glass of milk Mom will put down the spoon go over to the cabinet get a glass go to the refrigerator pour the milk hand it to Joey and then she will go back to the stove pick up the spoon and resume stirring the soup The soup stirring was interrupted by getting a glass of milk and then the soup stirring resumed This thing that most computers have is called an Interrupt and it works very much like what happened with Mom and Joey An interrupt starts with one more wire added to the IO Bus This wire is used by certain device adapters to let the CPU know that its a good time for the CPU to do an IO operation like right after someone presses a key on the keyboard When a device adapter turns the Interrupt bit on the next time the stepper gets back to step 1 the next instruction cycle will not do the usual fetch and execute but rather it will do of the following The result of this sequence is that the current IAR and Flags are saved to RAM addresses o and 1 and they are replaced with the contents of RAM bytes addresses 2 and 3 Then the CPU returns to its normal fetch and execute operation But the IAR has been replaced So the next instruction will be fetched from whatever address was in RAM byte 2 In other words what the CPU had been doing is saved and the CPU is sent off to do something else If at the end of this new activity the program puts RAM bytes o and l back into the IAR and Flags the CPU will pick up from exactly where it left off before it was interrupted This system is very useful for dealing with IO operations Without interrupts the program running in the CPU would have to make sure to check all of the devices on the IO Bus on a regular basis With interrupts the program can just do whatever it is designed to do and the program that deals with things like keyboard input will be called automatically as needed by the interrupt system We have not included this in our CPU because it would just make our Control Section wiring diagram too big It would need to add the following two more steps to the stepper wiring to do the above 8 steps in place of the normal instruction cycle paths for the Flags register to get to and from the bus a method of sending a binary o 1 2 or 3 to MAR and an instruction that restores RAM bytes o and 1 to the IAR and Flags register And that is an Interrupt system As far as the language is concerned the computer designers took an existing verb interrupt and used it in three ways It is a verb in the keyboard interrupted the program it is an adjective in This is the Interrupt system and it is a noun in the CPU executed an interrupt THATS ALL FOLKS Yes this is the end of our description of a computer This is all there is Everything you see a computer do is a long concatenation of these very simple operations the ADDing NOTting Shifting ANDing ORing XORing of bytes Storing Loading Jumping and IO operations via the execution of the instruction code from RAM This is what makes a computer a computer This is the sum total of the smarts in a computer This is all the thinking that a computer is capable of It is a machine that does exactly what it is designed to do and nothing more Like a hammer it is a tool devised by man to do tasks defined by man It does its task exactly as designed Also like a hammer if it is thrown indiscriminately it can do something unpredictable and destructive The variety of things the computer can be made do is limited only by the imagination and cleverness of the people who create the programs for them to run The people who build the computers keep making them faster smaller cheaper and more reliable When we think of a computer we probably think of that box that sits on a desk and has a keyboard mouse screen and printer attached to it But computers are used in many places There is a computer in your car that controls the engine There is a computer in your cell phone There is a computer in most cable or satellite television boxes The things that they all have in common are that they all have a CPU and RAM The differences are all in the peripherals A cell phone has a small keyboard and screen a microphone and a speaker and a twoway radio for peripherals Your car has various sensors and controls on the engine and the dials of the dashboard for peripherals The cash register in a fast food restaurant has a funny keyboard a small display screen and a small printer for receipts There are computers in some traffic lights that change the lights based on the time of day and the amount of traffic that crosses the sensors embedded in the roadway But the CPU and RAM make it a computer the peripherals can be very different For the rest of the book we will look at miscellaneous subjects related to understanding how computers are used a few interesting words that are related to computers some of their frailties and a few other loose ends HARDWARE AND SOFTWARE Youve heard of hardware That word has been around for a long time There have been hardware stores for a century or more I think that a hardware store originally sold things that were hard like pots and pans screwdrivers shovels hammers nails plows etc Perhaps hardware meant things that were made out of metal Today some hardware stores no longer sell pots and pans but they sell huge variety of hard things like bolts and lawnmowers also lumber and a lot of soft things too like carpet wallpaper paint etc But these soft things are not called software The word software was invented somewhere in the early days of the computer industry to differentiate the computer itself from the state of the bits within it Software means the way the bits are set on or off in a computer as opposed to the computer itself Remember that bits can be either on or off The bit has a location in space it is made of something it exists in space it can be seen The bit is hardware Whether the bit is on or off is important but its not a separate part that you bolt into the computer it is the thing in the computer that is changeable the thing that can be molded it is soft in that it can change but you cant pick it up in your hand all by itself This thing is called software Think of a blank videotape Then record a movie on it What is the difference between the blank videotape and the same videotape with a movie on it It looks the same it weighs the same you cant see any difference on the surface of the tape That surface is coated with very fine particles that can be magnetized In the blank tape the entire surface of the tape is magnetized in random directions After recording the movie on the tape some little places on the tape are magnetized in one direction and other little places are magnetized in the other direction Nothing is added to or taken away from the tape its just the way the magnetic particles are magnetized When you put the tape into a VCR it plays a movie The tape is hardware the pattern of the directions of magnetization on the tape is software In a computer there are a great many bits As we have seen a lot of bits have to be set in certain ways in order to make the computer do something useful The bits in the computer are always there If you want the computer to do a certain thing you set those bits on or off according to the pattern that will make the computer do what you want it to do This pattern is called software It is not a physical thing it is just the pattern in which the bits are set So the difference between hardware and software isnt like metal versus rubber Both metal and rubber are hardware as far as the computer definition is concerned Hardware is something you can pick up see handle Software is the way the hardware is set When you buy software it is recorded on something usually some kind of disk The disk is hardware the specific pattern recorded on that disk is software Another disk may look just like it but have completely different software written on it Another way to see the difference between hardware and software is how easy it is to send it across a distance If you have a vase that you want to send to your aunt Millie for her birthday you have to pack the vase in a box and have a truck take it from your house to her house But if you want to give her the present of music you might go to the store buy her a disk and mail it but you might also buy her a gift certificate on the Internet send her an email and have her download the music In that case the music will get to her house without a truck having to go there The music will be transported solely by the pattern of electricity that comes over the Internet connection to her house Another way to see the difference between hardware and software is how easy it is to make a copy of the item If you have a lawnmower and want a second lawnmower there is no machine that will copy the lawnmower You could photograph the lawnmower but youd only have a flat photograph of a lawnmower You couldnt mow any lawns with the photo To get a real second lawnmower youd have to go back to the lawnmower factory and build another one out of iron and plastic and rope and whatever else lawnmowers are made out of This is hardware Software can be copied easily by machine All you need is something that can read the disk or whatever it is recorded on and something else to write it onto a new disk The new one will be just like the original it will do all the same things If the original is your favorite movie the copy will also be your favorite movie If the original is a program that will prepare your tax papers so will the copy Software is not a physical thing it is just how the physical things are set By far the most commonly used definition of software is to refer to a package of computer instruction code I think that the way it got this name is that once you have built a device as versatile as a computer there are many different things that it can be made to do But when there are no instructions in it it cant do anything So the software is an absolutely necessary part of a computer that is doing some task It is a vital part of the total machine yet it isnt like any other part in the machine You cant weigh it or measure it or pick it up with a pair of pliers So it is part of the ware but it isnt hardware The only thing left to call it is software PROGRAMS As mentioned earlier a series of instructions in RAM are called a program Programs come in many sizes Generally a program is a piece of software that has everything needed to do a specific task A system would be something larger made up of several programs A program might be made up of several smaller parts known as routines Routines in turn may be made up of subroutines There are no hard and fast definitions that differentiate between system program routine and subroutine Program is the general term for all of them the only difference is their size and the way they are used There is another distinction between two types of programs that is not related to their size Most home and business computers have a number of programs installed on them Most of these programs are used to do something that the owner wants to do These are called application programs because they are written to apply the computer to a problem that needs to be solved There is one program on most computers that is not an application Its job is to deal with the computer itself and to assist the application programs This one program that is not an application is called the Operating System THE OPERATING SYSTEM An Operating System or OS for short is a large program that has many parts and several objectives Its first job is to get the computer up and running when you first turn the computer on Another one of its jobs is to start and end application programs and give each one time to run It is the boss of every other program on that computer When more than one program is in RAM it is the operating system that switches between them It lets one program run for a small fraction of a second then another program then another program If there are ten programs in RAM and each one gets to run for one hundredth of a second at a time each program would be able to execute millions of instructions in that time several times per second It would appear that all ten programs were running simultaneously because each one gets to do something faster than the eye can see An Operating system also provides services to application programs When an application program needs to read from or write to the disk or draw letters on the screen it does not have to do all of the complicated IO instructions necessary to accomplish the task The OS has a number of small routines that it keeps in RAM at all times for such purposes All an application needs to do to use one of these routines is to load up some information in the registers and then jump to the address of the proper OS routine Heres an example of how it might be done Lets say you want to draw a character on the screen First put the ASCII code of the desired character into R0 Then put row and column numbers of where you want it to appear on the screen into R1 and R2 And heres the tricky part You put the address of the next instruction of your application program into R3 Now just jump to the OS routine The routine will take care of all of the details of drawing the character on the screen and then its last instruction will be JMPR R3 Thus these routines can be called from any application and when done the routine will jump back to the next instruction in the application that called it There are several reasons for having the OS do all of the IO functions One is that it makes it easier to write application programs the programmer does not even need to know how the peripherals actually work Another reason is that it would waste a lot of RAM if every application had its own copy of all of the IO routines One of the most important reasons is that the OS can check to see whether the program should be allowed to do what it is asking to do This is part of the OSs other job of being the boss The heart of the OS is basically a loop of instructions that asks the following questions Do I need to input anything Do I need to output anything Do I need to let any program run Then it starts over again If the answers to all of these questions is no the CPU just executes the instructions in this loop over and over millions of times per second When there is something to do it jumps to the beginning of the program that takes care of it and when that is done it jumps back to this loop where the OS waits for something else to do Here is a diagram of our larger RAM version showing what parts of RAM might be occupied by an Operating System and several other programs Within each programs RAM there is all of the instruction code that makes the program work Each program maybe divided up into its own main loop and many routines that are used for the various tasks that it needs to do As mentioned the OS also has routines that can be called by other programs Each program also uses part of its address space for the data that it is working on The calculator for example needs to have a few bytes where it stores the numbers that the user enters into it Solitaire needs some bytes that specify which cards are in which positions The word processor needs some RAM for all of the ASCII codes that make up the document you are working on The OS also needs bytes where it can store fonts keep track of where application programs have been loaded receive the data that it reads from the disk and for many other purposes And so this is what goes on inside your average computer There are many different programs and data areas in RAM The OS jumps to a program the program jumps to a routine the routine jumps to a subroutine Each program works on its data or calculates something or does an IO operation As each one finishes it jumps back to where it came from The CPU executes one instruction from one program at a time and if they are written intelligently each program will get its job done piece by piece without interfering with the rest If our computer had included an interrupt system like we described a few chapters back every time someone pressed a key on the keyboard or moved the mouse there would be an interrupt that would call a part of the OS that determines which IO device caused the interrupt and then calls the proper routine to take care of whatever it was When that was done the CPU would continue on with the next instruction of whatever program had been running when the interrupt happened This can all seem very complex with so many millions and billions of instructions being executed in the blink of an eye There are ways of organizing programs and good programming practices that can make it much more understandable A study of these would simplify software in the same manner that I hope this book has simplified the hardware But that would be the subject for another entire book LANGUAGES Writing programs is very hard to do when youre just writing ones and zeros but that is the only code that the CPU understands What is a language A spoken language such as English is a way to represent objects actions and ideas with sounds A written language is a way to represent the sounds of a spoken language with symbols on paper Sounds like another code and a code representing a code We just cant get away from these things Do you remember that shorthand we used when we were looking at the CPU instruction code and the wiring in the Control Section Well that is actually something more than just a handy tool that was invented for this book It is a computer language Here are a few lines of it A computer language is a way to represent the instruction code Its purpose is to make it easier to write computer programs In order to use this language you write the program you want with ASCII characters and save it into a file Then you load a special program called a compiler into RAM and jump to its first instruction The compiler will read the ASCII file translate each line into the Instruction Code that it represents and write all of the Instruction Code bytes into a second file The second file may then be loaded into RAM and when the CPU jumps to its first instruction the program you wrote in ASCII will hopefully do what you intended it to do Of course when computers were first invented all programs had to be written directly in ones and zeros Then somebody got tired of the tedium of programming that way and decided to write the first compiler Then ever after programs were written in this easier language and then translated into Instruction Code by the compiler With the original compiler you could even write a better compiler So in order for a computer language to exist you need two things a set of words that make up the language another code and a compiler that compiles the written language into computer instruction code The language that we have seen in this book has only about 20 words in it Each word correlates directly to one of the instructions of which this computer is capable Each line you write results in one computer instruction When you write an 87 line program in this language the instruction code file that the compiler generates will have 87 instructions in it Then someone invented a higher level language where one line of the language could result in multiple computer instructions For example our computer does not have an instruction that does subtraction But the compiler could be designed so that it would recognize a new word in the language like SUB RA RB and then generate however many machine instructions were necessary to make the subtraction happen If you can figure out how to do something fancy with 47 instructions you can have a word in your language that means that fancy thing Then someone invented an even higher level language where the words that make up the language dont even resemble the CPUs actual instructions The compiler has a lot more work to do but still generates instruction code that does the things that the words in that language mean A few lines from a higher level language might look like this Balance 2000 Interest Rate 034 Print Hello Joe your interest this year is Print Balance X Interest Rate The compiler for this language would read this fourline program and generate a file that could easily contain hundreds of bytes of instruction code When that instruction code was loaded into RAM and run it would print Hello Joe your interest this year is 68 Writing software in higher level languages can result in getting a lot more done in a shorter amount of time and the programmer no longer needs to know exactly how the computer actually works There are many computer languages Some languages are designed to do scientific work some are designed for business purposes others are more general purpose Lower level languages are still the best for certain purposes THE FILE SYSTEM As we saw earlier the way a disk actually works is pretty foreign to most people who use a computer To make things easier someone invented an idea called a file A file is supposed to be similar to the kind of paper files that people use in offices A paper file is a sheet of cardboard folded in half and placed in a file cabinet This folder has a tab on it where you can write some sort of name for the folder and then you can put one or many pieces of paper in the folder A computer file is a string of bytes that can be any length from one byte up to all of the bytes available on the disk A file also has a name A disk may have many files on it each with its own name Of course these files are just an idea To make a file system work the operating system provides a bunch of software that makes the disk appear to be like a filing cabinet instead of having heads tracks sectors and blocks of bytes This file system gives application programs an easy way of using the disk Applications can ask the OS to create read write or erase something called a file All the application needs to know is the name of the file You open it request bytes send it bytes make it bigger or smaller close the file The OS uses part of the disk to maintain a list of file names along with the length of each file and the disk address head track sector of the first sector of the data If the file is smaller than a disk sector thats all you need but if the file is larger than one sector then there is also a list which contains as many disktype addresses as needed to hold the file The application program says create a file with the name letter to Jane Then the user types the letter to Jane and saves it The program tells the OS where the letter is in RAM and how long it is and the OS writes it to disk in the proper sector or sectors and updates the file length and any necessary lists of disktype addresses To use the file system there will be some sort of rules that the application program needs to follow If you want to write some bytes to the disk you would need to tell the OS the name of the file the RAM address of the bytes that you want to write and how many bytes to write Typically you would put all of this information in a series of bytes somewhere in RAM and then put the RAM address of the first byte of this information in one of the registers and then execute a Jump instruction that jumps to a routine within the Operating System that writes files to the disk All of the details are taken care of by this routine which is part of the OS If you ask the OS to look at your disk it will show you a list of all the file names and usually their sizes and the date and time when they were last written to You can store all sorts of things in files Files usually have names that are made up of two parts separated by a period like xxxxyyy The part before the period is some sort of a name like letter to Jane and the part after the dot is some sort of a type like doc which is short for document The part before the period tells you something about what is in the file The part after the dot tells you what type of data is contained in this file in other words what code it uses The type of the file tells both you and the OS what code the data in the file uses In one popular operating system txt means text which means that the file contains ASCII A bmp means BitMaP which is a picture A exe means executable which means it is a program and therefore contains Instruction Code If you ask the OS what programs are available to execute it will show you a list of the files that end with exe If you ask for a list of pictures that you can look at it will show you a list of files that end with bmp There are many possible file types any program can invent its own type and use any code or combination of codes ERRORS The computer is a fairly complex machine that does a series of simple things one after another very quickly What sorts of things could go wrong here In the early days of computing when each gate in the computer was relatively expensive to build sometimes there were components that actually had moving parts to make electrical connections Two pieces of metal had to touch to make the electricity go to where the builders wanted it to go Sometimes when the machine stopped working correctly the fixit guy would look inside to find out what was wrong and he would find that a spider had crawled inside the machine and had gotten itself wedged in between two of these pieces of metal that were supposed to touch each other Then when one piece of metal moved to touch the other the spider was in the way and they wouldnt touch So the electricity wouldnt get to where it needed to go and the machine would not operate correctly anymore The fixit guy would remove the bug clean up the contacts and report There was a bug in the computer And he literally meant a bug Over time whenever a computer appeared to be operating incorrectly people would say that the computer had a bug There are two main classes of computer bugs hardware and software A hardware bug actually means that the computer is broken This could be as serious as you turn the computer on and it catches fire to there is one byte in the RAM where one bit is always off Now one bit in RAM that refuses to change maybe a problem or it may not If the byte where that bit is located somehow never gets used then the computer will work just fine If that byte is part of a place where a name is stored then the name may get changed from Joe to Jod If that byte has some program instructions in it you may get an XOR instruction changed to a JMP instruction Then when the program gets to that instruction it will not do the XOR like it is supposed to but rather it will jump somewhere else and start executing whatever is at the new location as though it was a series of instructions The contents of those bytes will determine what happens next but it will almost certainly be as wrong as a train falling off its track If a gate is broken in the stepper for instance so that step 4 never comes on then the computer will not really be able to operate at all It would still be able to fetch instructions in steps 1 2 and 3 but every instruction would execute incorrectly Certainly the program would make a mess of things after executing just a few instructions Software bugs can take many forms but they are all ultimately programmer mistakes There are probably many more ways to write a program incorrectly than correctly Some errors just create some kind of incorrect results and other errors cause the computer to crash One of my favorite stupid programmer stories is this Someone bought a car on credit He got a coupon book with the loan one coupon to be sent in with each payment But when he made his first payment he accidentally used the last coupon in the book instead of the first one A few weeks later he received a computergenerated letter from the loan company saying Thank you for paying off your loan in full next time you need a loan please use us again Obviously the program just checked the coupon number and if it was equal to the highest number coupon in the book jump to the routine for a paidinfull loan It should have at least checked the balance remaining on the loan before deciding that it was paid off This is a subtle error it might not be caught by the loan company until they audited their books months later The computer did exactly what it was told to do and most of the time it was adequate but the program was not written to anticipate all of the situations that sometimes occur in the real world One of the worst software bugs is getting stuck in a loop The program executes a series of instructions and then jumps back to the beginning of the series and executes it over and over again Of course loops are used all the time in programming but they are used to do something that has a finite number of similar steps It may repeat until 50 bytes have been moved somewhere or keep checking for the user to press a key on the keyboard But the computer will exit the loop at some point and continue on to its next task But if there is some sort of programming error where there is a loop that has no way out the computer will appear to be completely stuck This is sometimes called being hung the whole computer may need to be turned off and restarted to get out of the loop and back into useful operation There are all sorts of errors that end up with the CPU trying to execute something other than instruction code Lets say you have your program residing at address 10 through 150 and you have some ASCII data such as names and phone numbers at addresses 151 through 210 If the program is written incorrectly so that under certain conditions it will jump to address 180 it will just continue fetching and executing the bytes starting at address 180 If 180189 was filled with the ASCII for Jane Smith the program will now be executing complete garbage a series of bytes that were not designed to be Instruction Code It may put itself into a loop or jump back somewhere into the program or issue the command to erase the disk drive And it will be doing garbage at its usual high speed If you looked at the patterns in the bytes you could see what it would do but it could be just about anything If the name at address 180 was Bill Jones it would do something completely different Since it is not designed to be useful most likely it will just keep making a bigger mess out of what is in memory until the computer will have to be powered off to get it to stop Another type of error could occur if a program accidentally wrote John Smith into the place where a font was stored In that case every letter E that got drawn on the screen thereafter would look like this The computer executes hundreds of millions of instructions every second and it only takes one wrong instruction to bring the whole thing to a screeching halt Therefore the subject of programming computers in a manner that will be completely bug free is something that gets a lot of attention Almost all programming is done with languages and the compilers for these languages are designed to generate Instruction Code that avoids the most serious types of errors and to warn the programmer if certain good programming practices are violated Still compilers can have errors and they will never be able to spot an error like the one above with the car loan As you can see the computer and its software are pretty fragile things Every gate has to work every time and every instruction that gets executed has to be correct When you consider all of the things that could go wrong the high percentage of things that normally go right is actually quite impressive COMPUTER DISEASES Another place where human characteristics get assigned to computers is something called a computer virus This implies that computers can come down with a disease and get sick Are they going to start coughing and sneezing Will they catch a cold or the chicken pox What exactly is a computer virus A computer virus is a program written by someone who wants to do something bad to you and your computer It is a program that will do some sort of mischief to your computer when it runs The motivation of people who write virus programs ranges from the simple technical challenge of seeing whether one is capable of doing it to a desire to bring down the economy of the whole world In any case the people who do such things do not have your best interests in mind How does a computer catch a virus A virus program has to be placed in your RAM and your computer has to jump to the virus program and run it When it runs it locates a file that is already on your hard disk that contains a program that gets run on a regular basis by your computer like some part of the operating system After the virus program locates this file it copies the virus program to the end of this file and inserts a jump instruction at the beginning of the file that causes a jump to where the virus program is Now your computer has a virus When a computer with a virus is running it does all of the things it is supposed to do but whenever it runs the program that contains the virus the inserted jump instruction causes the virus program to be run instead Now the virus usually will do something simple like check for a predetermined date and if it is not a match then the virus program will jump back to the beginning of the file where the operating system program still exists Thus your computer will appear totally normal there are just a few extra instructions being executed during its regular operations The virus is considered dormant at this point But when that date arrives and the virus decides to do whatever is in the rest of its program it can be anything When the virus program is running it can do whatever mischief the person who wrote it could think of It can erase files on your disk or send them somewhere else via the internet One humorous virus would every once in a while make the letters on the screen appear to come loose and fall into a pile at the bottom of the screen Heres an example of how to catch a virus Lets say that you have a friend who finds a funny movie on the Internet It makes him laugh and he thinks that you will enjoy it too so he emails the movie file to you You receive the movie file and play it and you do enjoy it There are two different things that could have occurred here If your friend sent you a file named funnymov and your OS includes a program that plays mov files then the OS will load that program into RAM and that program will read the pictures in the funnymov file and display them on your screen This is fine the program that ran was something that was already on your computer The funnymov file just provided a series of pictures that were displayed on your screen But if your friend sent you a file named funnyexe then when you ask the OS to play the movie it will load funnyexe into RAM and jump to its first instruction Now you have a program running in your computer that came from somewhere else If it is a virus program it will probably play the movie for you so that you dont suspect anything but it can do anything else that it wants to the files on your disk while you are watching the movie It will probably install itself and go into a dormant state for days or weeks and you wont even know that your computer is infected But sooner or later it will come alive and do whatever damage it was designed to do This sort of malicious program is called a virus because the way it works is similar to the way that real viruses infect living things A real virus is a thing that is smaller than a one celled animal It doesnt quite qualify as being alive because the virus by itself cannot reproduce They do reproduce however by invading a cell of something that is alive Once in the cell the virus uses the mechanisms of that cell to make copies of itself which can then go on and infect other cells The computer virus also cannot reproduce or do anything else by itself It needs to get into a computer and somehow get itself executed one time by that CPU When it runs that first time it inserts itself somewhere into the operating system so that it will thereafter get executed on a regular basis Those instructions will do whatever damage they are designed to do to the computer on which they are running and they will also usually do something that is designed to spread the virus to other computers FIRMWARE Of course RAM is an essential part of any computer The ability to write bytes into RAM and read them back out again is an integral part of how the machine works But in some computers there are sections of the RAM that only get written to when the computer starts up and thereafter these sections remain unchanged as the computer operates This could be true in any computer that always runs the same program Perhaps half of the RAM is used to contain the program and the other half of the RAM is used to contain the data that the program is working on The half with the program has to be loaded at some point but after that the CPU only has to read the bytes of the program in order to fetch and execute them When you have this sort of situation you can build half of your computers RAM the normal way and with the other half you skip the NAND gates and just wire each bit directly to an on or an off in the pattern of your program Of course you cant write into the prewired RAM but you can read from it just fine This type of RAM was given the name Read Only Memory or ROM for short You use it the same way you use RAM but you only read from it There are two advantages to ROM In the early days of computers when RAM was very expensive ROM was a lot less expensive than RAM The other advantage is that you no longer have to load the program into RAM when you first turn the computer on It is already there in ROM ready to be executed by the CPU The point here is a new word Since software was named soft because it is changeable when it comes to ROM you still have a pattern in the bits but theyre not so soft anymore You cant write into a ROM you cant change the bits And so this type of memory came to be known as firmware It is software that is permanently written into hardware But that isnt the end of the story The ROM described above had to be built that way at the factory Over the years this idea was improved and made easier to use The next advance was when someone had the bright idea of making ROM where every bit was set on at the factory but there was a way of writing to it with a lot of power that could burn out individual connections changing individual bits to an off Thus this ROM could be programmed after leaving the factory This was called Programmable ROM or PROM for short Then someone figured out how to make a PROM that would repair all of those broken connections if it were exposed to ultraviolet light for a half an hour This was called an Erasable PROM or EPROM for short Then someone figured out how to build an EPROM that could be erased by using extra power on a special wire built into the EPROM This was called Electrically Erasable PROM or EEPROM for short One particular type of EEPROM has the name Flash memory So there is RAM ROM PROM EPROM EEPROM and Flash These are all types of computer memory The thing they have in common is that they all allow random access They all work the same way when it comes to addressing bytes and reading out the data that is in them The big difference is that RAM loses its settings when the power goes off When the power comes back on RAM is full of all zeros The rest of them all still have their data after power off and back on You may ask then Why dont computers use EEPROM for their RAM Then the program would stay in RAM when the computer was off The answer is that it takes much longer to write into EEPROM than RAM It would slow the computer down tremendously If someone figures out how to make an EEPROM that is as fast and as cheap and uses the same or less power as RAM Im sure it will be done By the way the word ROM has also come to be used to mean any type of storage that is permanently set such as a pre recorded disk as in CD ROM but its original definition only applied to something that worked just like RAM BOOTS What do boots have to do with computers Well there is an old phrase that goes pull yourself up by your own bootstraps It is kind of a joke it literally refers to the straps that are sewn into many boots that are used to help pull the boots onto your feet The joke is that if you are wearing such a pair of boots and want to get up off the ground instead of getting a ladder or climbing a rope you can get yourself off the ground by simply pulling hard enough on those bootstraps Of course this would only work in a cartoon but the phrase has come to mean doing something when there is no apparent way to do it or doing something without the tools that would normally be used or accomplishing something by yourself without help from anyone else In a computer there is a problem that is similar to needing to get off the ground and having no tools available to accomplish it When a computer is operating the memory is full of programs that are doing something and when the operator of the computer enters a command to start another program the operating system locates the program on disk loads it into memory and jumps to the first instruction of the program Now that program is running But when you first turn on a computer how do you get the operating system into memory It takes a program running in memory to tell the disk drive to send over some instruction code and the program needs to write that code into memory at an appropriate place and then jump to its first instruction to get the new program running But when you turn the computer on every byte in memory is all zeros There are no instructions in memory at all This is the impossible situation you need a program in memory to get a program in memory but there is nothing there So in order for the computer to get going in the first place the computer has to do something impossible It has to pull itself up by its bootstraps A long time ago in the early days of computers the machine had switches and push buttons on the front panel that allowed the operator to enter bytes of data directly into the registers and from there into RAM You could manually enter a short program this way and start it running This program called a bootstrap loader would be the smallest possible program you could write that would instruct the computer to read bytes from a peripheral store them in RAM and then jump to the first instruction When the bootstrap loader executes it loads a much larger program into memory such as the beginnings of an operating system and then the computer will become usable Nowadays there are much easier ways of loading the first program into the computer in fact it happens automatically immediately after the computer gets turned on But this process still happens and the first step is called booting or booting up and it only means getting the first program into memory and beginning to execute it The most common solution to this problem has three parts First the IAR is designed so that when the power is first turned on instead of all of its bits being zero its last bit will be zero but the rest of its bits will be ones Thus for our little computer the first instruction to be fetched will be at address mi mo Second something like the last 32 bytes of the RAM 235256 will be ROM instead hardwired with a simple program that accesses the disk drive selects head o track o sector o reads this sector into RAM and then jumps to the first byte of it The third part then had better be that there is a program written on that first sector of the disk This sector by the way is called the boot record This word boot has become a verb in computer talk It means to load a program into RAM where there are no programs Sometimes people use it to mean loading any program into RAM but its original meaning only applied to loading the first program into an otherwise blank RAM DIGITAL VS ANALOG Youve no doubt heard these terms bandied about It seems that anything associated with computers is digital and everything else is not But thats not quite close enough to the truth What they mean is quite simple but where they came from and how they ended up in their current usage is not so straightforward The word digital comes from digit which means fingers and toes in some ancient language and since fingers and toes have been used for counting digital means having to do with numbers Today the individual symbols that we use to write numbers o 1 2 3 etc are called digits In the computer we represent numbers with bits and bytes One of the qualities of bits and bytes is their unambiguous nature A bit is either on or off there is no gray area in between A byte is always in one of its 256 states there is no state between two numbers like 123 and 124 The fact that these states change in steps is what we are referring to when we say digital The word analog comes from the same place as analogy and analogous thus it has to do with the similarity between two things In the real world most things change gradually and continuously not in steps A voice can be a shout or a whisper or absolutely anywhere in between When a telephone converts a voice into an electrical equivalent so that it can travel through a wire to another telephone that electricity can also vary everywhere between being fully on and fully off Sound and electricity are two very different things but the essence of the voice has been duplicated with electricity Since they are similar in that respect we can say that the electrical pattern is an analog of the voice Although the meaning of analog comes from this similarity factor when you make an analog you are usually making an analog of something that is continuously variable This idea of something being continuously variable has come to be the definition of analog when you are comparing digital and analog Something that is analog can be anywhere within the entirety of some range there are no steps Digital means change by steps and analog means change in a smooth continuous manner Another way to say it is that digital means that the elements that make up a whole come from a finite number of choices whereas analog means that a thing is made of parts that can be selected from an unlimited number of choices A few noncomputer examples may help to clarify this If you have a platform that is three feet above the floor you can either build stairs for people to climb up to it or a ramp On the ramp you can climb to any level between the floor and the platform on the stairs you only have as many choices as there are steps The ramp is analog the stairs are digital Lets say that you want to build a walkway in your garden You have a choice of making the walkway out of concrete or out of bricks If the bricks are three inches wide then you can make a brick walk that is 30 inches wide or 33 inches wide but not 31 or 32 If you make the walk out of concrete you can pour it to any width you want The bricks are digital the concrete is analog If you have an old book and an old oil painting and you want to make a copy of each you will have a much easier time making a copy of the book Even if the pages of the book are yellowed and the corners are dogeared and there are dirt smudges and worm holes inside as long as you can read every letter in the book you could retype the entire text exactly as the author intended it With the oil painting the original colors may have faded and are obscured by dirt The exact placement of each bristle in each brush stroke the thickness of the paint at every spot the way adjacent colors mix could all be copied in great detail but there would inevitably be some slight differences Each letter in the book comes from a list of a specific number of possibilities the variations of paint colors and their positions on the canvas are limitless The book is digital the painting is analog So there you have the difference between analog and digital The world around us is mostly analog Most old technologies were analog like the telephone phonograph radio television tape recorders and videocassettes Oddly enough though one of the oldest devices the telegraph was digital Now that digital technology has become highly developed and inexpensive the analog devices are being replaced one by one with digital versions that accomplish the same things Sound is an analog thing An old fashioned telephone is an analog machine that converts analog sound into an electrical pattern that is an analog of the sound which then travels through a wire to another phone A new digital telephone takes the analog sound and converts it into a digital code Then the digital code travels to another digital phone where the digital code is converted back into analog sound Why would anyone go to the trouble of inventing a digital phone when the analog phone worked just fine The answer of course is that although the analog phone worked it was not perfect When an analog electrical pattern travels over long distances many things can happen to it along the way It gets smaller and smaller as it travels so it has to be amplified which introduces noise and when it gets close to other electrical equipment some of the pattern from the other equipment can get mixed in to the conversation The farther the sound goes the more noise and distortion are introduced Every change to the analog of your voice becomes a part of the sound that comes out at the other end Enter digital technology to the rescue When you send a digital code over long distances the individual bits are subjected to the same types of distortion and noise and they do change slightly However it doesnt matter if a bit is only 97 on instead of 100 A gates input only needs to know whether the bit is on or off it has to decide between those two choices only As long as a bit is still more than halfway on the gate that it goes into will act in exactly the same way as if the bit had been fully on Therefore the digital pattern at the end is just as good as it was at the beginning and when it is converted back to analog there is no noise or distortion at all it sounds like the person is right nextdoor There are advantages and disadvantages to each method but in general the benefits of digital technology far outweigh its shortcomings Probably the biggest advantage of digital has to do with the making of copies When you make a copy of something like a vinyl record you could record it to a tape recorder or I guess you could even get all of the equipment to cut a new vinyl record But there will be some degree of difference between the original and the copy In the first place all machinery has accuracy limitations A copy of any physical object can be very close to the original but never quite exact Second if there are any scratches or particles of dust on the original the copy will then have duplicates of these defects Third friction between the record and the needle actually wears away a tiny amount of vinyl every time you play it If you use a tape recorder there is always a low level of hiss added to the sound If you make a copy of a copy and a copy of that etc the changes will get larger and larger at each stage When it comes to something that is digital as long as every bit that was on in the original is also on in the copy we get an exact copy every time You can make a copy of the copy and a copy of that etc and every one of them will be exactly the same as the original Digital is definitely the way to go if you want to be able to make an unlimited number of copies and preserve something for all time The computer and peripherals we have built are entirely digital so far And if all we ever wanted to do with them were digital things such as arithmetic and written language we could leave it that way However if we want our computer to play music and work with color photographs there is one more thing we need to look at I LIED SORT OF There is one piece of hardware in a computer that is not made completely out of NAND gates This thing is not really necessary to make a computer a computer but most computers have a few of them They are used to change from something that is analog to something that is digital or digital to analog Human eyes and ears respond to analog things Things that we hear can be loud or soft things that we see can be bright or dark and be any of a multitude of colors The computer display screen that we described above had 320 x 200 or 64000 pixels But each pixel only had one bit to tell it what to do to be on or off This is fine for displaying written language on the screen or it could be used to make line drawings anything that only has two levels of brightness But we have all seen photographs on computer screens First of all there needs to be a way to put different colors on the screen If you get out a magnifying glass and look at a color computer or television screen you will see that the screen is actually made up of little dots of three different colors blue red and green Each pixel has three parts to it one for each color When the display adapter scans the screen it selects all three colors of each pixel at the same time For a computer to have a color screen it needs to have three bits for each pixel so it would have to have three times the RAM in order to be able to control the three colors in each pixel individually With three bits each color could be fully on or off and each pixel would therefore have eight possible states black green red blue green and red yellow green and blue cyan blue and red magenta and green blue and red white But this is still not enough to display a photograph To do that we need to be able to control the brightness of each color throughout the range between fully on and fully off To do this we need a new type of part that we will describe shortly and we need more bits in the display RAM Instead of one bit for each color in each pixel we could have a whole byte for each color in each pixel Thats three bytes per pixel for a total of 192000 bytes of RAM just for this small display screen With these bytes using the binary number code you could specify 256 levels of brightness for each color in each pixel This would amount to 16777216 different states or colors for each pixel This is enough variety to display a reasonably goodlooking photograph In order to make this work a number specifying 256 different levels of brightness you need a thing called a digital to analog converter or DAC for short A DAC has eight digital inputs and one analog output The way it works is that it is wired up to treat the input as a binary number and the output has 256 levels between off and on The output has 256 gradations between off and on and it goes to the level that the input number specifies If the input is a 128 the output will be halfway on For a 64 the output will be one quarter on For 0 the output will be fully off In order to make this color screen work the display adapter needs to access three bytes at a time connect them to three DACs and connect the outputs of the DACs to the three colors in the current pixel being painted Thats how a color screen works When we defined analog in the last chapter we said that it was something that was continuously variable from fully off to fully on But our DAC really only has 256 different levels at its analog output Its a lot closer to being analog than a bit but it still has steps What the computer is doing is approximating an analog thing in steps small enough to fool the intended audience When it comes to the eye 256 different levels of brightness is sufficient If something requires smaller steps to fool the intended audience you can make a DAC that has 16 bits on the digital side Thus you can present the digital input with a number anywhere from o to 65535 The analog side can still only vary from fully off to fully on but the size of the steps will be much smaller since there are now 65536 of them When it comes to the ear it can hear very small differences and so a 16 bit DAC is required for high quality sound All sounds from music to speech to thunder crashes are vibrations of the air They vary in how fast the air vibrates and in exactly how it vibrates The human ear can hear vibrations from about 20 Hz at the low end to 20000 Hz 20 kHz at the high end so this is the range of vibrations that computers are designed to deal with For any electronic machine to make sounds there is a device called a speaker All that a speaker does is move back and forth in the air making the air vibrate If it makes the air vibrate in precisely the same way as the original thing that was recorded it will sound just like the original In order to store a sound in a computer the position of the speaker is divided into 65536 possible positions Then a second is divided into 44100 parts At each one of those parts of a second the desired position of the speaker is stored as a twobyte number This is enough information to reproduce sound with very high quality To play top quality stereo music a computer would need a sound peripheral This would have two 16 bit DACs with their analog outputs connected to speakers It would also have its own clock that ticks at 44100 Hz At each tick it would get the next two twobyte numbers and connect them to the digital side of the DACs As far as speed goes this would be 176400 bytes per second Certainly that is fast but remember that our computer clock ticks a billion times per second That means that the computer can send four bytes to the sound peripheral and go off and execute about 4000 instructions on some other task before it needs to send the next four For going the other way there is an Analog to Digital Converter or ADC for short This is used to convert the sound from a microphone into a series of bytes or for a camera to convert a picture into a series of bytes The input has one wire that can be anywhere from all the way off to all the way on The ADC makes its outputs into a number from 0255 for an 8bit ADC or from 065535 for a 16bit ADC This number represents how much the input is on or off Half on is 128 or 32768 one quarter on is 64 or 16384 etc This process is just the reverse of what a DAC does DACs and ADCs are not made out of NAND gates they have electronic parts like radios have How they do what they do is not a proper subject for this book So maybe I lied when I said that everything in a computer is made out of NAND gates Well not really because DACs and ADCs are only used in certain types of peripherals not in the computer itself FULL DISCLOSURE We have built a very small computer here It is about the smallest computer that could be invented that does everything necessary to be worthy of the name computer I dont think that anyone has built such a small computer since about 1952 and no one has ever built this exact computer in the real world If a real computer designer ever read this book Im sure hed be pulling his hair out over all of the opportunities that have been missed here to make a better machine But again the goal has been to illustrate computer principles as simply as possible This is an eightbit computer That means that the registers in the processor are eight bits the bus is eight bits and in this machine even the Memory Address Register is eight bits With most of the computers that actually get built while the individual bytes in RAM remain 8 bits everything else is expanded to 16 bits 32 bits or 64 bits or a combination of these in different parts of the machine Our RAM only has 256 bytes which is ridiculously small but thats all you can have with an eightbit Memory Address Register If you use 16 bits you can have 65536 bytes of RAM thats 64kb if you use 24 bits you can have 16mb if you use 32 bits you can have 4 gigabytes of RAM Real computers have things that this one does not but they are not capable of doing things that this computer cannot do In our computer if you want to shift a byte three bits to the left you would put three shift left instructions in your program In most real computers they have shifters that will shift any number of bits in one instruction But the result is the same your byte ends up looking the same in either case the real computer just gets the job done faster In our computer the adder can add two eightbit numbers If you want to add 16 bit numbers you have to employ some software to do it In most computers the adder can add 16 or 32 bit numbers in one instruction Again the results are the same one is just faster than the other The stepper in our computer is a simplification of something that most computers have called a state machine State machines provide steps but start the next instruction as soon as possible do what is necessary for an interrupt system can create more complex instructions etc Since all we needed was six consecutive steps we built a simpler thing and just made up the term stepper So yes our computer is a simple small relatively slow computer but it can do everything that more complicated machines can do The things that make a bigger machine bigger are designed to get the job done faster do it in fewer clock cycles do the same task with fewer instructions operate on several bytes at the same time But the nature of what the machines do is exactly the same Every task they can do comes down to shifting ANDing ORing XORing ADDing and NOTing bytes There are no other fancy types of operations that have been left out of this book In a bigger machine you can do addition subtraction multiplication and division in a single instruction That is because they have huge numbers of gates arranged into things like a hardware multiplier There is no reason to show you the details of how you construct one of these it is a very complicated job for the few people who need to build one It is understandable and it all ultimately comes down to NAND gates just like everything else But we have seen how to do all the math operations there are with just an adder shifter NOT gates and some software The hardware multiplier gets there faster but the results are exactly the same Bigger machines have more registers the registers are each multiple bytes they have adders that can add three numbers at the same time but still the instructions come down to the same simple operations Your understanding of computers is not small because we have looked at a small computer PHILOSOPHY Why do we have a chapter called Philosophy in a book about computers The only thing in this book that even comes close to being a philosophical question is its title But How do it Know We will attempt to answer this question a little later on This book has been about the computers that we have today But what about the future As computers and software continue to advance how soon if ever will the day come when there are walking talking computerized robots that look and act just like people Will the day come when we have to decide whether or not to give these robots the same legal rights as people Will computers eventually take over the world and replace people altogether To answer these sorts of questions people often refer to a major question that has been outstanding in the field of philosophy for many years The question is whether man is composed solely of the structural body that we can see and dissect or whether there is an integral spiritual component to every human being which accounts for the qualities of consciousness love honor happiness pain etc That question is far beyond the scope of this book and it remains unconvincingly answered despite many books arguing each viewpoint There are people in the sciences who say that we are on track to building conscious computers and it will happen There are people in the humanities who say that it is impossible because you cant manufacture a spirit Each side has been unable to sway the other If we define the brain as that funny looking chunk of gray meat enclosed by the skull and define the mind as whatever it is that is responsible for consciousness memory creativity thinking and everything else that we notice going on in our heads then we can restate the big philosophic question as Are the brain and the mind one and the same thing Then when it comes to the question about building a convincing human robot there would be two possibilities If the brain and the mind are the same thing you might not be able to build a synthetic person today but as time went on eventually you could understand every structure and function in the brain and build something of equal complexity that would generate true consciousness and that really should act just like any other person If the brain and the mind are not the same thing then building a robot buddy will always be about simulating humanity not building something of equal quality and value Restating the question doesnt make it any easier to answer but this idea of separating what we know about minds from what we know about brains may be useful Early on we said that we were going to show how computers work so that we could see what they were capable of doing and also what they were not capable of doing We are going to take what we know about brains and what we know about minds and compare each individually to our new knowledge about computers In doing so we can look for differences and similarities and we maybe able to answer a few less controversial questions Computers do certain things with great ease such as adding up columns of numbers A computer can do millions of additions in a single second The mind can barely remember two numbers at the same time never mind adding them up without a pencil and paper The mind seems to have the ability to look at and consider relatively large amounts of data at the same time When I think of my favorite cat I can re experience seeing what he looks like hearing the sounds of his purring and mewing feeling the softness of his fur and his weight when picked up These are some of the ways that I know my pet What would it mean for our computer to think about a cat It could have pictures of the cat and sounds of the cat encoded in files on a spinning disk or in RAM Is that thinking If you ran the bytes of these files one by one through the ALU would that be thinking If you put the picture on the screen would that be thinking If you played the sounds to the speakers would that be thinking The sounds and pictures encoded in the computer are just byte patterns sitting where they are They dont look like anything or sound like anything unless they are sent to the peripherals for which they were designed And if they are sent to the screen and speakers the computer doesnt see them or hear them Of course your computer could have a camera pointing at the screen and a microphone listening to the sounds but the computer still wouldnt see a picture or hear a sound it would just collect more strings of bytes very similar to the ones sent to the screen and speakers in the first place There could be programs that perform mathematical operations on the picture files in order to discover patterns and store the results of these calculations in other files There could be files that relate one picture file to other similar picture files and pictures to sounds etc creating more files But no matter how much programming is applied to the picture files there is something that the mind can do that the computer simply doesnt have any facility for The mind can consider the whole of some thing all at the same time You can think of the whole of the cat all at once Its sort of like the difference between the movie film and the TV screen The movie film has whole pictures the TV screen only has one pixel at a time You could say that your mind works so quickly that you dont notice the details it gets integrated into a whole just like the pixels get integrated into an entire picture But what does the integrating And when its integrated what is it and where is it And what looks at the integrated whole Weve just seen everything thats in a computer The computer moves one byte at a time over the bus The fanciest thing it does is to add two bytes into one Everything else it does amounts to nothing more than the simple warehousing of bytes A stored byte doesnt do anything beyond maintaining its own current setting A computer just doesnt have any facilities that integrate the elements of a picture into anything else nowhere to store that something else and nothing with which to look at it Im not saying that something couldnt be built that would perform these functions Im just saying that computers as we know them today dont currently include any such device Here is another question If a brain works like a computer then it needs to have a program for the CPU to run Where would this program come from Although the brain has trillions of cells the entire human body starts with one fertilized egg cell So any program that the brain has would have to be present in this single cell presumably in the DNA Scientists have now decoded the entire DNA sequence of humans DNA is interesting in that it is a long string of only four types of things Its digital A lot of the pieces of this string are used for making chemical reactions take place to make proteins etc but the majority of it is called junk DNA because no one knows what its purpose is But even if you consider that the entirety of the DNA is devoted to computer software then there could be about a billion instructions in this program Now thats a lot of software but the average home computer probably has that much software loaded onto its hard drive and that wouldnt be anywhere near enough to run a human being Some have said that the human computer programs itself As a programmer myself I just cant imagine how this would work While its true that a program can accumulate data and modify the way it works based on the collected data this is not the same thing as writing a new program If someone ever writes this program that can write any new needed program there will be a huge number of computer programmers put out of work forever Then there are the kinds of errors that computers make versus the kind that people make If a computer gets stuck in a loop it appears to have stopped completely Have you ever seen a person walking down the street suddenly stop working All functions just cease The person would just fall down until somehow his computer rebooted People do collapse from time to time but it is usually because some other part broke like having a heart attack and you can see the person recognize the pain as it takes them down But if the human computer got stuck in a loop there would be an instant loss of consciousness and the body would just fall completely limp with no struggle I have never seen that but if the brain operated just like a computer you would expect to see it on a fairly regular basis Then there is the matter of speed As we have seen a simple computer can do a billion things in a second When it comes to the brain it has nerves that have some similarity to the wires in computers Nerves can also carry electricity from place to place In a computer wires come out of gates and go into other gates In the brain nerves are connected together by synapses These synapses are spaces between nerves where the electricity in one nerve creates a chemical reaction which then causes the next nerve to create its own electricity These chemical reactions are painfully slow No one has shown that these nerves are connected up anything like the wires in a computer but their lack of speed makes it very unlikely that it would do much good even if the connections were similar After the electricity travels quickly through the nerve cell it reaches the synapse where the chemical reaction takes about one five hundredth of a second to complete That means that our simple computer built out of NAND gates could do two million things in the same time that only one thing could be done by a computer built out of nerves and synapses Another area where the difference between the mind and computers is quite obvious is in the area of recognizing faces The mind is very good at it If you walk into a party with fifty people present you will know in a matter of seconds whether you are among a group of friends or of strangers A lot of research has been done into how people accomplish this feat and a lot of very interesting information has been uncovered There is also a lot of speculation and there are many fascinating theories about the underlying principles and mechanisms But the complete and exact structures and functions have not been uncovered If you give a computer a picture file of a person and then give it the same file again it can compare the two files byte by byte and see that each byte in one file is exactly equal to the corresponding byte in the other file But if you give the computer two pictures of the same person that were taken at different times or from different angles or with different lighting or at different ages then the bytes of the two files will not match up byte by byte For the computer to determine that these two files represent the same person is a huge task It has to run very complex programs that perform advanced mathematical functions on the files to find patterns in them then figure out what those patterns might look like from different angles then compare those things to every other face it has ever stored on its disk pick the closest match then determine if its close enough to be the person or just someone that looks similar The point is that computers have a method of dealing with pictures based on the principles on which computers work Using these principles alone has not yet yielded computers or software that can recognize a face with anywhere near the speed and accuracy of any ordinary person Voice recognition by computers is another technology that has come a long way but has much further to go to rival what the mind does easily So in comparing a computer to a brain it just doesnt look very likely that they operate on the same principles The brain is very slow there isnt any place to get the software to run it and we dont see the types of problems we would expect with computer software errors In comparing a computer to the mind the computer is vastly better at math but the mind is better at dealing with faces and voices and can contemplate the entirety of some entity that it has previously experienced Science fiction books and movies are full of machines that read minds or implant ideas into them space ships with builtin talking computers and lifelike robots and androids These machines have varying capabilities and some of the plots deal with the robot wrestling with consciousness self realization emotions etc These machines seem to feel less than complete because they are just machines and want desperately to become fully human Its sort of a grownup version of the childrens classic Pinocchio the story about a marionette who wants to become a real boy But would it be possible to build such machines with a vastly expanded version of the technology that we used to build our simple computer Optimism is a great thing and it should not be squashed but a problem will not be susceptible to solution if you are using a methodology or technology that doesnt measure up to that problem In the field of medicine some diseases have been wiped out by antibiotics others can be prevented by inoculations but others still plague humanity despite the best of care and decades of research And lets not even look into subjects like politics Maybe more time is all thats needed but you also have to look at the possibility that these problems either are unsolvable or that the research has been looking in the wrong places for the answer As an example many visions of the future have included people traveling around in flying cars Actually several types of flying cars have been built But they are expensive inefficient noisy and very dangerous They work on the same basic principles as helicopters If two flying cars have any sort of a minor accident everyone will die when both cars crash to the Earth So todays aviation technology just wont result in a satisfactory flying car Unless and until someone invents a cheap and reliable antigravity device there will not be a mass market for flying cars and traffic on the roads will not be relieved If you want to build a machine that works just like a person certainly the best way to do it would be to find out how the person works and then build a machine that works on the same principles has parts that do the same things and is wired up in the same way as a person When Thomas Edison invented the phonograph he was dealing with the subject of sound Sound is a vibration of the air So he invented an apparatus that captured the vibrations in the air and transformed them into a vibrating groove on the surface of a wax cylinder The sound could then be recreated by transferring the vibrations in the groove back into the air The point is that in order to recreate sound he found out how sound worked and then made a machine that worked on the same principle Sound is a vibration the groove in a phonograph is a vibration A lot of research has been done on the subject of what makes people tick A lot of research has been done on the subject of how to make computers do the things that people do A lot of things have been discovered and a lot of things have been invented I do not want to minimize any of the work done or results achieved in these areas But there are many things that have not yet been discovered or invented Many dead brains have been dissected and their parts have been studied and classified The brain does contain nerve cells which move electricity from one place to another This is a similarity between brains and computers But research into the actual operation of living human brains is necessarily limited Most observations have been made during surgeries that were necessitated by accident or disease Many observations have been made of changes to behavior after an injury or disease has disabled certain parts of the brain From this research it has been possible to associate certain functions with certain areas of the brain But no one has discovered a bus a clock any registers an ALU or RAM The exact mechanism of memory in the brain remains a mystery It has been shown that nerves grow new connections over time and it is assumed that this is the mechanism of learning but no one has been able to say that this particular nerve does this exact function as we can do with the individual wires in a computer Everything that goes into a computer gets turned into one code or another The keyboard generates one byte of ASCII per keystroke a microphone generates 44100 binary numbers per second a color camera generates three binary numbers per pixel 30 times a second and so on No one has isolated the use of any codes like ASCII binary numbers fonts or an instruction code in the brain They maybe there but they have not been isolated No one has traced a thought or located a memory in the same way that we could follow the operation of a program in a computer It is widely assumed that the brain works in some much more spread out way than a single computer that there are thousands or billions of computer elements that cooperate and share the work But such elements have not yet been located In the world of computing this idea is called parallel processing and computers with dozens or hundreds of CPUs have been built But these computers still havent resulted in a human substitute Think of it all as a puzzle How people work is one side of the puzzle Making computers do things that people do is the other side of the puzzle Pieces of the puzzle are being assembled on both sides The problem is that as progress is being made on both sides it looks more and more like these are two different puzzles they are not coming together in the middle They are not converging into a single picture The researchers are very aware of these developments But when it comes to pop culture people hear about new inventions all the time and see the future portrayed in science fiction films and the logical conclusion seems to be that research will continue to solve the problems one by one until in 10 or 20 or 30 years we will have our electromechanical friends In the past century we conquered electricity flight space travel chemistry nuclear energy etc So why not the brain andor mind The research however is still at the stage where every time one new answer is found it creates more than one more new question So it appears that whichever way we look at it neither the brain nor the mind work on the same principles as computers as we know them I say as we know them because some other type of computer may be invented in the future But all of the computers we have today come under the definition of Stored Program Digital Computers and all of the principles on which they operate have been presented in this book Still none of this proves that a synthetic human could never be built it only means that the computer principles as presented in this book are not sufficient for the job Some completely different type of device that operates on some completely different set of principles might be able to do it But we cant comment on such a device until someone invents one Going back to a simpler question do you remember Joe and the Thermos bottle He thought that the Thermos had some kind of a temperature sensor and a heater and cooler inside But even if it had had all of that machinery in it it still wouldnt know what to do it would just be a mechanical device that turned on the heater or cooler depending on the temperature of the beverage placed in it A pair of scissors is a device that performs a function when made to do so You put a finger and thumb in the holes and squeeze The blades at the other end of the scissors move together and cut some paper or cloth or whatever it is that you have placed in their way Do the scissors know how to cut shapes out of paper or how to make a dress out of cloth Of course not they just do what theyre told Similarly NAND gates dont know what they are doing they just react to the electricity or lack of it placed on their inputs If one gate doesnt know anything then it doesnt matter how many of them you connect together if one of them knows absolutely zero a million of them will also know zero We use a lot of words that give human characteristics to our computers We say that it knows things We say it remembers things We say that it sees and understands Even something as simple as a device adapter listens for its address to appear on the IO bus or a jump instruction decides what to do There is nothing wrong with this as long as we know the truth of the matter Now that we know what is in a computer and how it works I think it is fairly obvious that the answer to the question But How do it Know is simply It doesnt know anything Adder 79 address 66 ALU 87 AND gate 20 ASCII 37 bit 10 bus 42 Bus 1 90 byte 34 carry 80 character 36 Clock 93 code 28 comparator 82 CPU 67 decoder 48 device adapter 149 Enabler 40 fetch 112 flag 132 gate 15 IO Bus 146 InputOutput 146 Instruction Address Register 110 Instruction Code 115 Instruction Cycle 111 Instruction Register 110 Interrupt 167 logic 85 machine language 140 memory 24 25 NAND gate 21 NOT gate 20 OR gate 69 peripherals 146 program 111 Random Access Memory 53 Read Only Memory 191 Register 41 shifter 73 stepper 99 Tally Marks 58 virus 188 XOR gate 70 Do computers seem confusing Are computers impossible to understand Are computers a complete mystery What exactly are computers doing on the inside Does it seem like computers must be magic Did you ever wonder how computers actually work What are the essential parts that make up a computer Can computers think like the way people do How can computers do so many different things Did you ever just wonder But How Do It Know Finally heres a book that really explains how computers work Computers are far simpler than anyone has ever permitted you to believe This book is written to clearly identify computers for everyone It contains everything you need to know and nothing you dont need to know No technical background of any kind is required But How Do I Know starts at the beginning and presents the complete essentials of what it takes to make a computer It presents every piece and part in the proper order so that each one can be understood easily and effortlessly Every part is explained fully and every important idea is introduced when first This book is about the essentials of everything It is about seeing the series of ideas that resulted in this invention that we all call computer But How Do It Know leaves no doubt as to how the parts of a computer work together and the reader will have the very simple picture of exactly what a computer is If you want to turn on a light or a fan you never need to understand how computers work