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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.

How it works

Fingers are given the following values:

• Holding one's right hand as a fist = 0
• One's thumb = 1 = (2^1-1)
• One's index finger = 2 = (2^2-1)
• One's middle finger = 4 = (2^3-1)
• One's ring finger = 8 = (2^4-1)
• One's little finger = 16 = (2^5-1)
• One's left hand little finger = 32 = (2^6-1)
• One's left hand ring finger = 64 = (2^7-1)
• One's left hand middle finger = 128 = (2^8-1)
• One's left hand index finger = 256 = (2^9-1)
• One's left hand thumb = 512 = (2^10-1)
• All of both hand's fingers = 1023 = (2^11-1−1)
• Any combination = the fingers that are up's number + all other fingers that are up's numbers

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

Understanding the basic of Binary

Binary is composed of 1's and 0's. It adds itself up the greater the number of bits (or digits - for comparison), from right to left, the same way decimal does. In decimal you have 1, 2, to 9, then add 1 to the left side and a 0 to the right. Thus 10 is next - and so on. In binary you count the same way, only there are just 0-1, instead of 0-9, so when you get to the max of 1 - you then add 1 to the left and a 0 to the right and get 10. Which if you count in decimal, as you do it, it would be 2. Continue to count in decimal as your binary bits get higher, and you can keep track of the numbers the way you usually count. In decimal, which is base 10(binary is base 2). Base and a number, indicates how many unique digits that counting method has.

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:

Two Hands

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

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

Fractions

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

Using two hands:

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.

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.)

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.

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.

It is also possible to represent balanced ternary numbers in this manner.

Multiple levels of counting (instead of curling)

Each time you count to your 10th finger, it is one level. Each finger - of yours - may be capable of 5 different positions, which you can test of yourself. If you can do 5 positions on each finger, then you can count in double Trinary. Trinary up to (3^10-1) = 19683 or up to (3^10-1*2) = 39,366 because trinary can do 0, 1, and 2 - on your highest finger.

But it doesn't stop there, next you can count trinary 1 more time. With 5 finger positions, you can count to 2 twice. Once from your base position of all fingers down, then from that level's highest position to position 4 and 5, then representing 1, and 2 again. Thus you can count to your 10th finger twice - making it 2 levels high. This gives you a max of 20 digits. Therefore your equation would be (3^20-1*1) for your 4th position of finger which is = 1,162,261,467. And your 5th position finger would be (3^20-1*2). Use a calculator and find out what that is.

Next you can count with binary up to a max of 5 finger positions. Thus 5 levels are possible. 0, 1, 2, 3, and 4. Can you figure out what this will be, using the above equations with this new possibility? Use a calculator and try to figure it out. It's more rewarding when you do it yourself. But if not, read on.

With 5 levels of binary you would have 40 bits of possibility. Therefore the equation would be, (2^40-1) for your 40th bit(or digit position) which equals = 549,755,813,888. To find out what it would be with all fingers in the max position you would use (2^41-1-1) = 1,099,511,627,775. To find out what any organic array of finger positions represents, you would take the base (2) to the power of finger position-1 (^x-1) + all other finger positions (2^y-1) + (2^z-1) and so on ... and you would arrive at what the decimal equivalent to the binary representation that you showed was.

See also

• Chisanbop
• Binary numeral system
• Base 5

External links

• How to count to 1,023 on your fingers

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