Finger binary

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Finger binary is a system for counting and displaying binary numbers on the fingers and thumbs of one or more hands. It is possible to display all numbers from 0 through 1023 (2¹⁰−1) if both hands are used.

1 How it works
2 Visualizing Finger Binary
3 Two Hands
4 Fractions
5 X-Y Coordinates
6 Buffering
7 The curling of fingers
8 See also
9 External links

[edit] How it works

Fingers are given the following values:

Holding one's hand as a fist = 0
One's thumb = 1
One's index finger = 2
One's middle finger = 4
One's ring finger = 8
One's little finger = 16

0	2	3 = 2 + 1	6 = 4 + 2
7 = 4 + 2 + 1	14 = 8 + 4 + 2	16	17 = 16 + 1
26 = 16 + 8 + 2	28 = 16 + 8 + 4	30 = 16 + 8 + 4 + 2	31 = 16 + 8 + 4 + 2 + 1
128 (if the right hand has the least significant bits)	256	448 = 256 + 128 + 64	480 = 256 + 128 + 64 + 32
512	544 = 512 + 32	768 = 512 + 256	992 = 512 + 256 + 128 + 64 + 32

[edit] Visualizing Finger Binary

Imagine this set of five 1s is your right hand, palm facing your face (High State):

11111

Your clenched right fist (Low State):

00000

Each finger has a value double of that immediately to the right of it, so we have the following:

	Pinky	Ring	Middle	Index	Thumb
Value	16	8	4	2	1

[edit] Two Hands

It is possible to use a second hand to continue from the first.

Left Hand					Right Hand
Thumb	Index	Middle	Ring	Pinky	Pinky	Ring	Middle	Index	Thumb
512	256	128	64	32	16	8	4	2	1

Combining this, all numbers from 0-1023 can be displayed (2¹⁰ = 1024 possible permutations) see also Binary numeral system.

[edit] Fractions

There is no reason why fractions cannot be represented. This time use the left hand to represent fractional binary:

	Thumb	Index	Middle	Ring	Pinky
Value	1/2	1/4	1/8	1/16	1/32

Using two hands:

Left Hand					Right Hand
Thumb	Index	Middle	Ring	Pinky	Pinky	Ring	Middle	Index	Thumb
1/2	1/4	1/8	1/16	1/32	1/64	1/128	1/256	1/512	1/1024

For example, using the left hand only, I am signing thumb-middle-pinky. I first read left-to-right and find the last finger is pinky (1/32). Then, reading right-to-left in whole-number binary, I read 21. Therefore, the fraction reads 21/32.

[edit] X-Y Coordinates

Simple vectors can be represented using (left-hand, right-hand) as an ordered pair of coordinates (x, y) on a 32x32 grid. The signer stands facing in the direction of the y-axis and the right side of the signer is along the x-axis. So, signing (thumb-index-ring, pinky-thumb) represents (26, 17), 26 units to the right and 17 units forward (relative to the signer.)

[edit] Buffering

This exercise requires a signer and a reader facing each other. The signer signs a random number (palms facing self). In order for the reader to sign the same as the signer, the reader begins by holding their hands in front of their own face. The reader crosses their arms at their forearms and faces their palms to the signer. The reader can then duplicate the signer and the reader will have buffered the signer.

[edit] The curling of fingers

It is possible to use the orientation of the fingers to count to even greater numbers, although one could not represent numbers such as 1025 because this would involve using the same finger for different digits.

	Hand 1						Hand 2
	Fist	Thumb	Index	Middle	Ring	Little finger	Little finger	Ring	Middle	Index	Thumb
Normal	0	1	2	4	8	16	32	64	128	256	512
Curled		1024	2048	4096	8192	16384	32768	65536	131072	262144	524288