|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{No footnotes|date=January 2009}}
| | The writer is recognized by the name of Figures Lint. My working day job is a librarian. California is our birth place. To gather cash is what her family members and her enjoy.<br><br>Here is my blog ... [http://www.neweracinema.com/tube/blog/74189 at home std test] |
| '''Finger binary''' is a system for [[Finger counting|counting]] and displaying [[Binary numeral system|binary numbers]] on the [[finger]]s of one or more [[hand]]s. It is possible to count from 0 to 31 (2<sup>5</sup>−1) using the fingers of a single hand, or from 0 through 1023 (2<sup>10</sup>−1) if both hands are used.
| |
| | |
| == Mechanics ==
| |
| {{see|Binary numeral system}}
| |
| | |
| 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]]. 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|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 [[digit (anatomy)|anatomical digits]] to represent [[numerical digit]]s 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:
| |
| | |
| {| class="wikitable" style="text-align:center"
| |
| |-
| |
| ! !![[little finger|Pinky]] !![[ring finger|Ring]] !![[middle finger|Middle]] !![[index finger|Index]] !![[Thumb]]
| |
| |-
| |
| !Power of two
| |
| |2<sup>4</sup> || 2<sup>3</sup> || 2<sup>2</sup> || 2<sup>1</sup> || 2<sup>0</sup>
| |
| |-
| |
| !Value
| |
| |16 || 8 || 4 || 2 || 1
| |
| |}
| |
| | |
| And when both hands are used:
| |
| | |
| {| class="wikitable" style="text-align:center"
| |
| |-
| |
| !rowspan=2|
| |
| !colspan=5| Left hand
| |
| !colspan=5| Right hand
| |
| |-
| |
| !Thumb !!Index !!Middle !!Ring !!Pinky
| |
| !Pinky !!Ring !!Middle !!Index !!Thumb
| |
| |-
| |
| !Power of two
| |
| |2<sup>9</sup> || 2<sup>8</sup> || 2<sup>7</sup> || 2<sup>6</sup> || 2<sup>5</sup> || 2<sup>4</sup> || 2<sup>3</sup> || 2<sup>2</sup> || 2<sup>1</sup> || 2<sup>0</sup>
| |
| |-
| |
| !Value
| |
| | 512 || 256 || 128 || 64 || 32 || 16 || 8 || 4 || 2 || 1
| |
| |}
| |
| | |
| 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 [[coordinate]]s, or sports scores (such as for [[table tennis]] or [[baseball]]).
| |
| | |
| === Examples ===
| |
| ==== Right hand ====
| |
| <gallery> | |
| Image:LSQ a.jpg|'''0'''
| |
| Image:Index finger.JPG|'''2'''
| |
| Image:LSQ v.jpg|'''6''' = 4 + 2
| |
| Image:Tri prsta.jpg|'''7''' = 4 + 2 + 1
| |
| Image:LSQ 6.jpg|'''14''' = 8 + 4 + 2
| |
| Image:LSQ i.jpg|'''16'''
| |
| Image:I love you in Sign Language or the number 19 in Finger Binary.jpg|'''19''' = 16 + 2 + 1
| |
| Image:LSQ 8.jpg|'''26''' = 16 + 8 + 2
| |
| Image:LSQ 9.jpg|'''28''' = 16 + 8 + 4
| |
| Image:LSQ 4.jpg|'''30''' = 16 + 8 + 4 + 2
| |
| Image:LSQ 5.jpg|'''31''' = 16 + 8 + 4 + 2 + 1
| |
| </gallery>
| |
| ==== Left hand ====
| |
| <gallery> | |
| Image:Chinesische.Zahl.Eins.jpg|'''256'''
| |
| Image:Chinesische.Zahl.Drei.jpg|'''448''' = 256 + 128 + 64
| |
| Image:Chinesische.Zahl.Vier.jpg|'''480''' = 256 + 128 + 64 + 32
| |
| Image:Thumbs up.jpg|'''512'''
| |
| Image:Chinesische.Zahl.Sechs.jpg|'''544''' = 512 + 32
| |
| Image:Chinesische.Zahl.Acht.jpg|'''768''' = 512 + 256
| |
| Image:Chinesische.Zahl.Fuenf.jpg|'''992''' = 512 + 256 + 128 + 64 + 32
| |
| </gallery>
| |
| | |
| == Negative numbers and non-integers ==
| |
| | |
| {{more|Binary numeral system#Representing real numbers}}
| |
| | |
| 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 2^10 - 1 in both positive and negative numbers (-1023 to +1023, with positive and negative zero still represented).
| |
| | |
| === 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: <math>\tfrac{1}{2^x}</math>. (These are known as [[dyadic fraction]]s.)
| |
| | |
| Using the left hand only:
| |
| | |
| {| class="wikitable" style="text-align:center"
| |
| !
| |
| !Thumb !!Index !!Middle !!Ring !!Pinky
| |
| |-
| |
| !Value
| |
| |1/2 || 1/4 || 1/8 || 1/16 || 1/32
| |
| |}
| |
| | |
| Using two hands:
| |
| | |
| {| class="wikitable" style="text-align:center"
| |
| |-
| |
| !colspan=5| <big>Left Hand</big>
| |
| !colspan=5| <big>Right Hand</big>
| |
| |-
| |
| !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
| |
| |}{{clear}}
| |
| | |
| [[File:Chinesische.Zahl.Acht.jpg|thumb|right|3/4, in fractional finger binary]]
| |
| 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 [[Equivalent fractions|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]].
| |
| | |
| For instance, if the thumb and index finger on the left hand are the only raised digits, the rightmost raised finger (the index finger) becomes "1". The thumb, to its immediate right, is now the 2s digit; added together, they equal 3. The index finger's original value (1/4) determines the denominator: the result is 3/4.
| |
| | |
| ==== Rational numbers ====
| |
| | |
| Combined [[integer]] and fractional values (i.e., [[rational number]]s) can be represented by setting a [[radix point]] somewhere between two fingers (for instance, between the left and right pinkies). All digits to the left of the radix point are integers; those to the right are fractional.
| |
| | |
| === Decimal fractions and vulgar fractions ===
| |
| | |
| [[Dyadic fraction]]s, explained above, unfortunately 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 (0.3330078125), but the conversion between dyadic and [[decimal fraction|decimal]] (0.333) or [[vulgar fraction|vulgar]] (1/3) 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 fraction]]s 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 (as well as 0).
| |
| | |
| == Finger ternary ==
| |
| | |
| In theory, it is possible to use other positions of the fingers to represent more than two states (0 and 1); for instance, a [[ternary numeral system]] ([[number base|base]] 3) could be used by having a fully raised finger represent 2, fully lowered represent 0, and "curled" (half-lowered) represent 1. This would make it possible to count up to 59,048 (3<sup>10</sup>−1) on two hands. In practice, however, many people will find it difficult to hold all fingers independently (especially the middle and ring fingers) in more than two distinct positions.
| |
| | |
| ==See also==
| |
| *[[Chisanbop]]
| |
| *[[Senary#Finger counting]]
| |
| | |
| ==References==
| |
| * {{cite book|last=Pohl|first=Frederik|title=Chasing Science|publisher=Macmillan|date=2003|edition=reprint, illustrated|page=304|isbn=978-0-7653-0829-0|url=http://books.google.com/books?id=XsLXJMagfmUC&pg=PA187&dq=fingers+binary+1023#PPA187,M1}}
| |
| * {{cite book|last=Pohl|first=Frederik|title=The Best of Frederik Pohl|publisher=Sidgwick & Jackson|date=1976|page=363|url=http://books.google.com/books?id=fDxbAAAAMAAJ&q=fingers+binary+1023&dq=fingers+binary+1023&pgis=1}}
| |
| * {{cite book|last=Fahnestock|first=James D.|title=Computers and how They Work|publisher=Ziff-Davis Pub. Co.|date=1959|page=228|url=http://books.google.com/books?id=j_0mAAAAMAAJ&q=fingers+binary+1023&dq=fingers+binary+1023&pgis=1}}
| |
| *
| |
| | |
| ==External links==
| |
| <!-- * [http://www.intuitor.com/counting/ How to count to 1,023 on your fingers] -->
| |
| * [http://www.instructables.com/id/Binary-Counting/ Binary Counting]
| |
| | |
| {{Gestures}}
| |
| | |
| [[Category:Finger counting|Binary]]
| |
| [[Category:Elementary arithmetic]]
| |