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# Finger Binary (was: Numerals in Conlangs)

From: John Cowan Thursday, August 12, 1999, 3:13
```Steg Belsky scripsit:

> Finger-binary is more compact than just plain counting on your fingers,
> since you can get up to 31 with only one hand.
I suggest that you count in gray code instead, because it only
involves moving one finger at a time.  With binary, you may have
to move all your fingers at once, as when going from 15 to 16.

Here's how gray code works.  Start by doing two fingers.
Count 0 as 00, count 1 as 01, count 2 as 11, count 3 as 10.

Then you count from 4 to 7 by raising the third finger and
running the above list backwards:
count 4 as 110, count 5 as 111, count 6 as 101, count 7 as 100.

Then you count from 8 to 15 by raising the fourth finger and
running the *whole* list above backwards.
count 8 as 1100, count 9 as 1101, count 10 as 1111, count 11 as 1110,
count 12 as 1010, count 13 as 1011, count 14 as 1001, count 15 as 1000.

Then you count from 16 to 31 by raising the fifth finger and
running the *entire* list above backwards.
count 16 as 11000, count 17 as 11001, count 18 as 11011, count 19 as 11010,
count 20 as 11110, count 21 as 11111, count 22 as 11101, count 23 as 11100,
count 24 as 10100, count 25 as 10101, count 26 as 10111, count 27 as 10110,
count 28 as 10010, count 29 as 10011, count 30 as 10001, count 31 as 10000.

And so on till you run out of fingers (at 1023) or patience.

--
John Cowan                                   cowan@ccil.org
I am a member of a civilization. --David Brin
```