pozorvlak (pozorvlak) wrote,

Counting in hexadecimal on your fingers

A simple and occasionally handy trick which deserves to be better known.

Use your thumb as a pointer, and your finger joints and fingertips to represent the numbers. Thus:
  • Thumb pointing to base of index finger = 0
  • Thumb pointing to first joint of index finger = 1
  • Thumb pointing to second joint of index finger = 2
  • Thumb pointing to tip of index finger = 3
  • Thumb pointing to base of middle finger = 4
  • Thumb pointing to tip of little finger = F = 15
By using both hands, you can either have a counter with two hex digits (so you can count from 0 to 255), or two separate counters. You can use the same trick to count in base 12: ignore the fingertips, and just count on the joints. A nice side-effect of counting like this (as I discovered this afternoon) is that to casual observers you look like you're meditating: hold your hands palm upwards and stare at something for the full effect.

I learned this trick from an early chapter of Georges Ifrah's monumental Universal History of Numbers, the bulk of which has sat accusingly unread on my bookshelves since roughly 2002. While it looks fascinating, it's also about six inches thick (it's spread over three volumes), and thus is rather intimidating. The trick was listed as one of the ways in which pre-literate peoples count: the general rule is "by enumerating parts of their bodies in a predefined sequence", but the number and sequence of the parts varies from people to people (though less than you'd think). Base sixteen isn't as common a number base as 10 or 12, but it's far from unknown. Another interesting titbit from the book was the list of independent reinventions of "Roman" numbers: it seems that they're essentially the obvious way of counting using notches on a stick after "one notch per item" becomes unwieldy.

[Totally confused by this entry? Hexadecimal notation (or base 16) is a way of writing numbers down. In ordinary decimal notation, each column describes numbers ten times the size of the numbers in the column to its right; the sequence is ... thousands, hundreds, tens, units, tenths, hundredths, ... . In hexadecimal, each column describes numbers sixteen times the size of the numbers in the column to its right. This has all sorts of uses in computing and electronics. For more, see here.]

Edit: Reddit thread. And it seems I was totally wrong in thinking this technique was confined to preliterate people - it's extremely common throughout the Indian subcontinent, and probably further afield! I do like it when I learn something new from comments on a blog post. See the comments below for more finger-counting techniques (and yes, I already know about the sodding binary technique, I just choose not to use it because it's extremely uncomfortable for me. Happy? :-) ).
Tags: computers, ideas, maths
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