On the subject of numbers, here’s a mathematical joke.

**There are 10 types of people in the world: those who understand binary and those who don’t.**

This joke can be extended. There are 10 types of people in the world: those who get this joke and those who don’t.

I suppose the ones who don’t get it can be divided into 10 categories too: those who don’t understand binary (and thus don’t stand a chance of getting it) and those who do understand binary but who don’t have a sense of humour.

If you’re one of the people who gets the joke, do you have a smug sense of self-satisfaction about the fact? Don’t worry, that’s nothing to feel guilty about. It’s all part of the whole business of humour, and is one of the reasons why humour is so satisfying.

If you don’t get the joke because you don’t understand binary, here’s a quick explanation of what binary is.

In our everyday numbering system there are ten individual digits: 0,1,2,3,4,5,6,7,8,and 9.

When you’re counting, once you’ve reached 9 you extend the sequence by starting all over again with the same numbers, but adding a digit in front of them to signify that you’re on a new sequence – so you get 10 to 19. Then you extend the sequence again, to 20 and 29 and so on.

There’s no particular mathematical reason why numbers go up to nine and then start repeating. We use that system essentially because we’ve got ten fingers. This system is based on ten digits (zero and the numbers one to nine), and it’s described as being to the base ten.

We could just as easily use a system in which the only digits are 0,1,2,3,4 and 5. In this case, once you’ve counted up to the number 5 you can’t simply go on to the number 6 as you can in the ten digit system – because there isn’t one. Instead, because you’ve run out of digits, you have to extend the sequence just as you did after reaching 9 with the ten digit system – by starting the sequence again with an extra digit in front of it. So you have to go back to the figure zero and precede it with a one. This number is written as “10”, but it isn’t the number ten in the familiar ten digit system, even though it looks like it: here it represents the number six. (In this six digit system the number ten is written as a one followed by a four, or “14”.)

That example of a numbering system had six digits, but you can equally have a system that only has TWO digits. While the six digit system lacked the digits 6, 7, 8 and 9, the two digit system lacks ALL OF THEM except for zero and one. While with the six digit system you had to start a new sequence after the number five (because there is no number six), with the two digit system you have to start a new sequence after the number one (because there is no number two). The number two is therefore written as a zero preceded by a one – as “10”.

This two digit system is what we refer to as the binary system (binary meaning two).

So, the number “10” in the binary system is the same number as the 2 in our normal, ten digit system.

The number “10” in the joke is actually the binary way of representing the number 2. That’s the core of the joke.

Having waded through this explanation you probably won’t suddenly find the joke hilariously funny, because an essential part of the enjoyment of a joke is the satisfaction of “getting it”. But at least you’re now prepared for the next binary joke that comes along. I’ve been told that there are 101101 of them – rather thin on the ground in other words.

Binary is the numbering system that is used in computers and other electronic equipment – because electronic equipment can only ‘recognise’ two states with which to build up numbers: on or off. (While we have ten fingers with which to do it.)