Why computers use binary

A photo, a song, and a message from your mate all arrive at your phone the same way. Not as pictures, or sound, or words, but as a stream of electrical pulses that are either on or off. Nothing in that wire knows what a photo is. Two states is the whole vocabulary, and somehow it is enough for a film, a song, and every word you have ever typed. So the interesting question is not how a computer stores a picture. It is how anything at all survives being cut down to on and off.

Start with the counting system you already use, because binary is the same idea with fewer digits to play with.

You count in denary, also called decimal, and that is base ten. You get ten digits, zero up to nine, and when you run out of them you start a new column to the left. That is all a base is. It is how many digits you are allowed before you need another column. Binary is base two. Two digits, zero and one, and that is the lot. You run out after one, so the columns pile up quickly, which is why binary numbers look so long on the page. Hexadecimal is base sixteen. Sixteen digits, so after nine it borrows the letters A to F to do digit duty. Why anyone would want sixteen digits has its own video: Why hexadecimal exists, C S oh one, oh three.

Three patterns are on the screen now. Only one of them could possibly be a binary number. Which one is it, and what rules the other two out?

Take your pick. I'll wait.

The answer is the middle one, one zero one one. Binary has exactly two digits, so the two sitting in the first pattern cannot be there. And B is a hexadecimal digit. It is perfectly legal in base sixteen, and meaningless in base two.

So the name of a base is really a count of its digits. Ten for denary, two for binary, sixteen for hexadecimal.

Here is the question every class asks at this point, and most textbooks skip it. Why not use ten states, the way we do.

Inside the machine a number is not written down anywhere. It is a voltage on a wire, and voltage is a messy thing. It sags along a long wire, it drifts as the chip warms up, and it gets nudged by interference from everything nearby. To hold a digit from zero to nine you would need ten different voltage levels, squeezed into the range the chip can produce. The gap between that is a six and that is a seven would be a sliver.

So picture the two designs side by side. Ten levels, or only two, on a chip that is warming up in your pocket. Which one would you back to be read correctly, millions of times every second?

Have a think. I'll wait.

Two, comfortably. With only off and on, the two states sit at opposite ends of the range, so the interference would have to be enormous before an off got mistaken for an on.

And two states is exactly what the hardware already gives you. A transistor is a switch: current flowing, or current not flowing. A computer works in binary because binary is what its own components are. Ten states would cost more to build and would be easier to misread. Two states are cheap, and they are hard to get wrong.

The second big idea is about meaning, and it is the one that makes the rest of this chapter make sense.

On the screen are eight bits. A bit is one of those on-or-off values, one digit of binary, and these eight are going to stay exactly where they are while we read them three different ways. Read as a whole number, that pattern is sixty-five. Getting from one to the other is a method, and the method belongs to the next video: Denary to binary and back, C S oh one, oh two. Read as a character, using the code computers agree on for text, the very same pattern is a capital A. That code is taught in Character sets and ASCII, C S oh two, oh two. Read as part of a picture, it is a row of eight pixels in a black and white image, where zero is white and one is black. White, black, five more white, then black.

Same eight bits, three completely different things. So what does that pattern actually mean on its own?

Take your time. I'll wait right here.

On its own, it means nothing at all. That pattern is not sixty-five, and it is not a letter A. It becomes one of them the moment a program decides how to read it.

So the bits do not know what they are. That is your sentence for this video, and it comes in two halves: two states in the wire, and meaning in the program. And it is not only your files that live like that. The instructions in a program are stored the same way, as bit patterns in memory. A photo, a song, and the code that opens them are all the same kind of thing down there.

This topic is examined in sentences rather than sums, so the wording is worth a minute of your time. Take a question like this one. Explain why a computer represents data in binary. Here are two answers, and both of them come from someone who understands the idea. The first says: because computers only understand ones and zeros. That hands the question straight back. It says binary is used because binary is used, and it names nothing physical at all. The second says: a transistor has two states, on and off, so those two values are all the hardware can hold, and two levels can still be told apart when the voltage drifts. That one names the component and gives the reason. One more piece of wording, and it is a pair of words people swap by accident. Data is the raw value: the bit pattern on the screen, or the number sixty-five sitting on its own. Information is that same value once a meaning has been attached to it. Sixty-five as somebody's age is information. The pattern is the data, and the reading of it is what makes it information.

Before the end, let me gather this into three sentences. One: a base is simply how many digits you are allowed, so ten for denary, two for binary, and sixteen for hexadecimal. Two: a computer works in two states because a transistor is a switch, and two voltage levels stay readable while everything around them drifts. Three: a pattern of bits carries no meaning by itself, and the program decides whether it is a number, a letter, a pixel, or an instruction. And the sentence to keep hold of, one more time: two states in the wire, and meaning in the program.

If that landed, drop a thumbs up on this one. It marks the videos you have properly nailed, so when you come back to this chapter later you can see at a glance what is left to do. If it has not landed yet, leave it un-thumbed and save the video instead. Ideas like this one often click on a second watch a few days later, and the un-thumbed ones are your own list of what to come back to.

Next in the chapter: Denary to binary and back. That one takes today's idea and turns it into a method, so you can put an everyday number into binary columns and read it back out again.

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