Tuesday, March 19, 2013

Counting to 1023 With Your Fingers

Everyone is taught from an early age to count with their fingers. The trouble is that it only works for numbers of 10 or less. Or, does it!...

In fact, anyone with ten fingers can easily use them to count to 1023 ($2^{10} - 1$).

Make two fists. That is zero. Lift only your right thumb: 1 ($2^0$), only right index: 2 ($2^1$), right thumb and right index: 3 ($2^0 + 2^1$), only right middle: 4 ($2^2$), and so on.

This way, any whole number less than 1023 can be represented. Suppose you wanted 783. That would look like:

What? I'm an engineer, not an artist.
 ($783 = 512 + 256 + 8 + 4 + 2 + 1 = 2^9 + 2^8 + 2^3 + 2^2 + 2^1 + 2^0$)

This is probably not the most intuitive way for most people, but that might just be a result of their upbringing. If this was the way you learned to count, I bet it would seem perfectly natural. Either way, it is certainly more useful.

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