Bi-quinary coded decimal: Difference between revisions

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[[Image:Soroban.JPG|349x349px|thumb|[[Soroban|Japanese abacus]]. The right side represents {{formatnum:1234567890}} in bi-quinary: each column is one digit, with the lower beads representing "ones" and the upper beads "fives".]]

'''Bi-quinary coded decimal''' is a [[numeral system|numeral encoding scheme]] used in many [[abacus]]es and in some [[Early computer|early computers]], includingnotably the [[Colossus computer|Colossus]].<ref>{{cite web|url=https://www.youtube.com/watch?v=thrx3SBEpL8&list=WL&index=17&t=0s |archive-url=https://ghostarchive.org/varchive/youtube/20211212/thrx3SBEpL8| archive-date=2021-12-12 |url-status=live|title=Why Use Binary? - Computerphile |publisher=YouTube |date=2015-12-04 |access-date=2020-12-10}}{{cbignore}}</ref> The term '''''bi-quinary''''' indicates that the code comprises both a two-state (''bi'') and a five-state (''quin''ary) component. The encoding resembles that used by many abacuses, with four beads indicating the five values either from 0 through 4 or from 5 through 9 and another bead indicating which of those ranges (which can alternatively be thought of as +5).

Several human languages, most notably [[Fula language|Fula]] and [[Wolof language|Wolof]] also use biquinary systems. For example, the Fula word for 6, ''jowi e go'o'', literally means ''five [plus] one''. [[Roman numerals]] use a symbolic, rather than positional, bi-quinary base, even though [[Latin]] is completely decimal.

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The Korean finger counting system [[Chisanbop]] uses a bi-quinary system, where each finger represents a one and a thumb represents a five, allowing one to count from 0 to 99 with two hands.

One advantage of one bi-quinary encoding scheme on digital computers is that it must have 2two bits set (one in the binary field and one in the quinary field), providing a built -in [[checksum]] to verify if the number is valid or not. (Stuck bits happened frequently with computers using [[Relay|mechanical relays]].)

==Examples==

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* [[George Stibitz|Stibitz]]<ref name="Stibitz_1957"/><!-- In this book Stibitz claims that he invented this code some years after inventing Excess-3 --> relay calculators at Bell Labs from [[Bell Labs#Calculators|Model II]] onwards

* [[FACOM 128]] relay calculators at [[Fujitsu]]

===IBM 650===

{{anchor|IBM650code}}<!--link from IBM 650 article-->

The [[IBM 650]] uses seven bits: Twotwo ''bi'' bits: (0 and 5) and five ''quinary'' bits: (0, 1, 2, 3, 4), with error checking.

* [[IBM 650]] – seven bits

: Two ''bi'' bits: 0 5 and five ''quinary'' bits: 0 1 2 3 4, with error checking.

: Exactly one ''bi'' bit and one ''quinary'' bit is set in a valid digit. In the pictures of the front panel below and in close-up, the bi-quinary encoding of the internal workings of the machine are evident in the arrangement of the lights – the ''bi'' bits form the top of a T for each digit, and the ''quinary'' bits form the vertical stem.

: (the machine was running when the photograph was taken and the active bits are visible in the close-up and just discernible in the full panel picture)

: Exactly one ''bi'' bit and one ''quinary'' bit is set in a valid digit. In the pictures of the front panel below and in close-up, theThe bi-quinary encoding of the internal workings of the machine are evident in the arrangement of theits lights – the ''bi'' bits form the top of a T for each digit, and the ''quinary'' bits form the vertical stem.

{| cellpadding="5" class="wikitable"

{| cellpadding="5" class="wikitable"

|-

|! Value || 05-01234 bits<ref name="Ledley_1960"/>

| rowspan="11" | [[File:IBM-650-panel.jpg|thumb|center|IBM 650 front panel while running, with active bits just discernible]]

[[File:IBM 650 panel close-up of bi-quinary indicators.jpg|thumb|center|Close-up of IBM 650 indicators while running, with active bits visible]]

|-

| 0 || 10-10000

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| 9 || 01-00001

|}

* [[Remington Rand 409]] - five bits

:One ''quinary'' bit (tube) for each of 1, 3, 5, and 7 - only one of these would be on at the time.

:The fifth ''bi'' bit represented 9 if none of the others were on; otherwise it added 1 to the value represented by the other ''quinary'' bit.

:(sold in the two models [[UNIVAC 60]] and [[UNIVAC 120]])

* [[===Remington Rand 409]] - five bits===

{| cellpadding="5" class="wikitable"

The [[Remington Rand 409]] has five bits: one ''quinary'' bit (tube) for each of 1, 3, 5, and 7 - only one of these would be on at the time. The fifth ''bi'' bit represented 9 if none of the others were on; otherwise it added 1 to the value represented by the other ''quinary'' bit. The machine was sold in the two models [[UNIVAC 60]] and [[UNIVAC 120]].

{| cellpadding="5" class="wikitable"

|-

|! Value || 1357-9 bits

|-

| 0 || 0000-0

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| 9 || 0000-1

|}

* [[===UNIVAC Solid State]] – four bits===

The [[UNIVAC Solid State]] uses four bits:One one ''bi'' bit: (5), three binary coded ''quinary'' bits: (4 2 1)<ref name="Steinbuch_1962"/><ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref name="Savard_2018_Decimal"/> and one [[parity bit|parity check bit]]

{| cellpadding="5" class="wikitable"

|-

|! Value || p-5-421 bits

|-

| 0 || 1-0-000

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| 9 || 1-1-100

|}

===UNIVAC LARC===

* [[UNIVAC LARC]] – four bits<ref name="Savard_2018_Decimal"/>

The [[UNIVAC LARC]] has four bits:One<ref name="Savard_2018_Decimal"/> one ''bi'' bit: (5), three [[Johnson counter]]-coded ''quinary'' bits and one parity check bit.

{| cellpadding="5" class="wikitable"

|-

|! Value || p-5-qqq bits

|-

| 0 || 1-0-000