All your bases

when you commonly work in base ten (that is 9+1, not F+1 or 1+1), you can sometimes miss interesting artefacts of numbers or dismiss them as being just facts or oddities.

One thing that's interested me over the years was the childhood realisation that the nine times table "went up" one side, and "came down" the other.

It wasn't until I grew up and started trying to think about problems from different points of view that I stumbled across the fact that this situation is true for all number bases.

so, in hexadecimal, if you take the nine as being ten-1, the F times table looks much like the nine times table you had as a kid.

 1 x F =  F
 2 x F = 1E
 3 x F = 2D
 4 x F = 3C
 5 x F = 4B
 6 x F = 5A
 7 x F = 69
 8 x F = 78
 9 x F = 87
 A x F = 96
 B x F = A5
 C x F = B4
 D x F = C3
 E x F = D2
 F x F = E1
10 x F = F0

This can be quite a revelation for some people. Funnily enough, it works right down to binary.

 1 x 1 =  1
10 x 1 = 10

okay, that was a poor maths joke, so now I'll just get my coat.