Why hexadecimal exists

Someone reads a colour code down the phone to you, and it arrives as twenty-four ones and zeros in a row. Somewhere around the twelfth digit you lose your place, and the colour you write down is not the colour they meant. That same colour, written the other way, is six characters long: one, B, nine, A, A, A. Identical value, identical information, and this time you can say it out loud without counting.

This is video three of nine in Binary and number bases. If today feels shaky, C S oh one, oh two, Denary to binary and back, is the one to go back to first.

Start with the problem hexadecimal was built to fix, because the machine does not actually have this problem. Inside the computer everything is binary, for solid reasons that C S oh one, oh one, Why computers use binary, goes through properly. But people have to read those values as well. Programmers, technicians and designers all end up staring at raw values while they chase a fault. And the human eye slides straight off a long row of identical symbols. You drop a digit, or you double one, or you start a column late, and the value you copied is not the value you were given. You have almost certainly met the shorthand already without noticing. Colour codes in a design app, the address printed on a network card, memory addresses inside an error message. All of those are written in the same sixteen-digit system, which is called hexadecimal, or hex when people are in a hurry. Three short codes are on screen. Four D two. Nine G one. A zero F. One of the three cannot possibly be hexadecimal. Pick one. I'll wait. It is nine G one, because G is not a hexadecimal digit at all. Hex runs zero to nine, then A, B, C, D, E and F, and it stops dead at F. Sixteen digits, no more and no fewer, and that count is what everything else in this video hangs off.

Base sixteen was not picked at random, and the reason it was picked is the point of the whole topic. Ordinary counting is base ten, with ten digits running zero to nine. Binary is base two, with two digits, zero and one. Hexadecimal is base sixteen. Sixteen digits means sixteen single characters, and we only own ten number symbols, so the last six borrow letters. A stands for ten, and F stands for fifteen. Now for sixteen rather than twelve or twenty. Sixteen is two to the power of four, so one hexadecimal digit covers exactly four bits, with nothing spare and nothing missing. Four bits is half a byte. So one hexadecimal digit is half a byte, and two hexadecimal digits are one whole byte, every time, with no rounding anywhere in it. That is your handle for this video, and it is worth saying out loud: one digit, four bits; two digits, one byte. Base eight does the same trick with three bits, and computers really did use it, but three does not divide into eight evenly, so hexadecimal is the one that stayed.

A single byte shows that fit better than any amount of explaining does. Here is one byte: one, one, zero, one, one, zero, one, zero. Eight characters, and you are already counting them with your finger. Chop it down the middle. One, one, zero, one on the left. One, zero, one, zero on the right. Two halves, four bits in each. Each half is one hexadecimal digit. The left half is written as D, the right half is written as A, so the whole byte is D A. How you turn a half into its digit is a conversion, and this video leaves that alone on purpose. C S oh one, oh five, Binary and hexadecimal, teaches it in both directions, and C S oh one, oh four, Denary and hexadecimal, comes at it from ordinary numbers. What matters here is the shape of the result. Eight characters became two, and every byte behaves the same way, so the writing shrinks to a quarter of the length. Both of those writings are the number two hundred and eighteen. Nothing about the value moved when the writing got shorter. Which leads to the thing most often misunderstood about hexadecimal. The machine never sees D A. Storage, memory and the processor are all still holding one, one, zero, one, one, zero, one, zero, exactly as before. Hexadecimal is a way of writing binary down for people. It is notation rather than storage, and the number of bits held underneath is identical either way. The value belongs to the machine, and the way it is written belongs to us, and hexadecimal is only ever the writing.

Edexcel put this exact idea on a paper in twenty twenty-five, and the wording of the question is where it turns sharp. Their Principles of Computer Science paper said that hexadecimal is used to represent memory addresses, then asked candidates to give two characteristics of hexadecimal notation. The examiner report on that question is on screen now, in their own words. Candidates sometimes confused the benefits of using hexadecimal with its characteristics, giving the benefits of using hexadecimal rather than focusing on its intrinsic characteristics. So there are two columns here and they are not interchangeable. A characteristic is what hexadecimal is. A benefit is why a person would choose to use it. The command word at the front of the question decides which column your answer comes from, and an answer from the wrong column earns nothing, however true it is. Four statements are on screen. It uses the digits zero to nine and A to F. It is quicker to write than binary. Each digit represents four bits. It is easier to spot a typing mistake. Put each one into a column. Have a go at this one. I'll wait. The first and the third are characteristics: the digit set, and one digit standing for four bits. The second and the fourth are benefits: quicker to write, and easier to spot a mistake. That same report warns about vague answers as well. Saying that hexadecimal uses letters is not enough on its own, because the answer wanted is the letters A to F, alongside the digits zero to nine. The next part of that question asked candidates to explain one reason why programmers use hexadecimal to specify memory addresses, and the report noted this. A number of candidates wrote that hexadecimal took less storage space than binary which is incorrect - the amount of bits required to store the value is identical. That is the point from earlier in this video, coming back in an examiner's own words: fewer characters on the page, and the very same bits underneath. Boards split on this one. A Q A and Edexcel both ask why hexadecimal is used, in words, on a written paper. O C R sets the conversions instead. So an O C R student is not asked this directly, but the conversions ahead make far more sense once you know what hexadecimal is actually for.

Right, let me put the video back together, and the chant goes first: one digit, four bits; two digits, one byte. Hexadecimal is base sixteen, and its digits run zero to nine and then A to F. That is what it is. One digit covers four bits and two digits cover a byte exactly, which is why base sixteen was chosen ahead of anything else. It is shorter, easier to read aloud and easier to copy without slipping, and those are benefits rather than characteristics. And underneath the writing nothing has changed, because the machine is still storing the same binary, bit for bit.

That list on screen is the whole chapter, and the thumbs-up landing on each row is a marker you leave for yourself. It means you are comfortable with that one and never need to watch it again. So give this one a thumbs-up if it landed. If it did not quite, leave it and save the video or the playlist instead, because this sort of thing often clicks on a second watch a few days on.

Next in the chapter is Denary and hexadecimal, which teaches the conversion this video deliberately left alone.

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