At last – a use for football?

I was trying to explain why an internet page used ‘F’ as part of the colour designation. “it’s because it is a hex number” I unhelpfully suggested. “How can F be a number?” was the instant reply.

I was surprised as this was a technically savvy user. So I tried to explain the rationale behind using ‘labels’ on a set of binary combinations and realised that I learnt hex as a Unix user as part of the package without really thinking too deeply.

It all stems from Binary, and I suggested that he think about the World cup, 1 winner, 2 finalists, 4 semi-finalists, 8 quarter-finalists, 16 round qualifiers, 32 top of pool teams. Each step is a doubling (or halving) of the teams. So in the same way we have in ’colums’ 1,2,4,8,16,32.

The real trick though is understanding that binary is not a left-to-right read. It is a right-to-left read so the world cup draws would actually be 32,16,8,4,2,1

If you want to express the world cup winner in a way that is simple, take the first ‘column’ and turn this from 0  to 1. As there are two finalists you make the first column 0 and the second 1 making a representation of 10. Third would be a 1 + 2 so that would represented as 11.

This continues and as you add more teams you may want to represent the whole 32 so you can position every team. Therfore to be fourth becomes 100 and so on. Twentieth is 16 + 4 so 10100. Thinking of it in that sense let him see that 16 isn’t actually a number, but a state, a ‘label’ for a binary code of 10000. It also helped him understand the funny numbers used, 512 1024 etc. in computing terms. It is a lot easier to put F on a keyboard input than 010000.

So as a Rugby Union fan I can at last say that football does indeed have some use!

Comments are closed.