But How Do It Know? - the Basic Principles of Computers for Everyone (30 page)

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 dog-eared, and there are dirt smudges and worm holes inside, as long as you can read every letter in the book, you could re-type 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 doesn’t matter if a bit is only 97% on instead of 100%. A gate’s 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 half way 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 next-door.

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 64,000 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. That’s three bytes per pixel, for a total of 192,000 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 16,777,216 different states (or colors) for each pixel. This is enough variety to display a reasonably good-looking 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. That’s 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. It’s 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 0 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 20,000 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 44,100 parts. At each one of those parts of a second, the desired position of the speaker is stored as a two-byte 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 44,100 Hz. At each tick, it would get the next two two-byte numbers, and connect them to the digital side of the DACs.

As far as speed goes, this would be 176,400 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 0-255 for an 8-bit ADC or from 0-65,535 for a 16-bit ADC. This number represents how much the input is on or off. Half on is 128 or 32,768, one quarter on is 64 or 16,384, 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 don’t 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, I’m sure he’d 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 eight-bit 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.