Finger binary is a system for counting and displaying binary numbers on the fingers of one or more hands. It is possible to count from 0 to 31 using the fingers of a single hand, from 0 through 1023 if both hands are used, or from 0 to 1,048,575 if the toes on both feet are used as well.
Mechanics
In the binary number system, each numerical digit has two possible states 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. : The rightmost digit represents two to the zeroth power ; the digit to its left represents two to the first power ; the next digit to the left represents two to the second power ; and so on. 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 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, and all fingers lowered is 0. In the two-handed system, all fingers raised is 1,023 and two fists 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.
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 -511 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.
Fractions
There are multiple ways of representing fractions in finger binary.
Dyadic fractions
Fractions can be stored natively in a binary format by having each finger represent a fractional power of two:. Using the left hand only:
Pinky
Ring
Middle
Index
Thumb
Value
1/2
1/4
1/8
1/16
1/32
Using two hands: The total is calculated by adding all the values in the same way as regular finger binary, then dividing by the largest fractional power being used, 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 /1024 = 768/1024 = 3/4. If using only one hand, it would be /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 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. For instance, if the thumb and index finger on the left hand are the only raised digits, the rightmost raised finger becomes "1". The thumb, to its immediate left, is now the 2s digit; added together, they equal 3. The index finger's original value determines the denominator: the result is 3/4.
Rational numbers
Combined integer and fractional values can be represented by setting a radix pointsomewhere betweentwo fingers. All digits to the left of the radix point are integers; those to the right are fractional.
s, explained above, have limited use in a society based around decimal figures. A simple non-dyadic fraction such as 1/3 can be approximated as 341/1024, but the conversion between dyadic and decimal or vulgar forms is complicated. Instead, either decimal or vulgar fractions can be represented natively in finger binary. Decimal fractions can be represented by using regular integer binary methods and dividing the result by 10, 100, 1000, or some other power of ten. Numbers between 0 and 102.3, 10.23, 1.023, etc. can be represented this way, in increments of 0.1, 0.01, 0.001, etc. Vulgar fractions can be represented by using one hand to represent the numerator and one hand to represent the denominator; a spectrum of rational numbers can be represented this way, ranging from 1/31 to 31/1.
Finger ternary
In theory, it is possible to use other positions of the fingers to represent more than two states ; for instance, a ternary numeral system could be used by having a fully raised finger represent 2, fully lowered represent 0, and "curled" represent 1. This would make it possible to count up to 59,048 on two hands. In practice, however, many people will find it difficult to hold all fingers independently in more than two distinct positions.
