Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: that is, up to 25−1 or 210−1 respectively.
Modern computers typically store values as some whole number of 8-bit bytes, making the fingers of both hands together equivalent to 1 bytes of storage—in contrast to less than half a byte when using ten fingers to count up to 10.
Mechanics
In the binary number system, each numerical digit has two possible states (0 or 1) and each successive digit represents an increasing power of two.
Note: What follows is but one of several possible schemes for assigning the values 1, 2, 4, 8, 16, etc. to fingers, not necessarily the best. (see below the illustrations.): The rightmost digit represents two to the zeroth power (i.e., it is the "ones digit"); the digit to its left represents two to the first power (the "twos digit"); the next digit to the left represents two to the second power (the "fours digit"); and so on. (The decimal number system is essentially the same, only that powers of ten are used: "ones digit", "tens digit" "hundreds digit", etc.)
It is possible to use anatomical digits to represent numerical digits by using a raised finger to represent a binary digit in the "1" state and a lowered finger to represent it in the "0" state. Each successive finger represents a higher power of two.
With palms oriented toward the counter's face, the values for when only the right hand is used are:
When only the left hand is used:
When both hands are used:
And, alternately, with the palms oriented away from the counter:
The values of each raised finger are added together to arrive at a total number. In the one-handed version, all fingers raised is thus 31 (16 + 8 + 4 + 2 + 1), and all fingers lowered (a fist) is 0. In the two-handed system, all fingers raised is 1,023 (512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1) and two fists (no fingers raised) represents 0.
It is also possible to have each hand represent an independent number between 0 and 31; this can be used to represent various types of paired numbers, such as month and day, X-Y coordinates, or sports scores (such as for table tennis or baseball). Showing the time as hours and minutes is possible using 10 fingers, with the hour using 4 fingers (0-23) and the minutes using 6 fingers (0-59).
Examples
Right hand
Left hand
When used in addition to the right.
Negative numbers and non-integers
Just as fractional and negative numbers can be represented in binary, they can be represented in finger binary.
Negative numbers
Representing negative numbers is extremely simple, by using the leftmost finger as a sign bit: raised means the number is negative, in a sign-magnitude system. Anywhere between and +511 can be represented this way, using two hands. Note that, in this system, both a positive and a negative zero may be represented.
If a convention were reached on palm up/palm down or fingers pointing up/down representing positive/negative, you could maintain 210 −1 in both positive and negative numbers ( to +1023, with positive and negative zero still represented).
Fractions
Dyadic fractions
Fractions can be stored natively in a binary format by having each finger represent a fractional power of two: . (These are known as dyadic fractions.)
Using the left hand only:
Using two hands:
The total is calculated by adding all the values in the same way as regular (non-fractional) finger binary, then dividing by the largest fractional power being used (32 for one-handed fractional binary, 1024 for two-handed), and simplifying the fraction as necessary.
For example, with thumb and index finger raised on the left hand and no fingers raised on the right hand, this is (512 + 256)/1024 = 768/1024 = 3/4. If using only one hand (left or right), it would be (16 + 8)/32 = 24/32 = 3/4 also.
The simplification process can itself be greatly simplified by performing a bit shift operation: all digits to the right of the rightmost raised finger (i.e., all trailing zeros) are discarded and the rightmost raised finger is treated as the ones digit. The digits are added together using their now-shifted values to determine the numerator and the rightmost finger's original value is used to determine the denominator.