Bi-quinary coded decimal is a numeral encoding scheme used in many

abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hin ...

es and in some early computers, including the

Colossus Colossus, Colossos, or the plural Colossi or Colossuses, may refer to: Statues * Any exceptionally large statue ** List of tallest statues ** :Colossal statues * ''Colossus of Barletta'', a bronze statue of an unidentified Roman emperor * ''Col ...

. 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 either 0 through 4 or 5 through 9 and another bead indicating which of those ranges. Several human languages, most notably

Fula Fula may refer to: *Fula people (or Fulani, Fulɓe) *Fula language (or Pulaar, Fulfulde, Fulani) **The Fula variety known as the Pulaar language **The Fula variety known as the Pular language **The Fula variety known as Maasina Fulfulde *Al-Fula ...

and

Wolof Wolof or Wollof may refer to: * Wolof people, an ethnic group found in Senegal, Gambia, and Mauritania * Wolof language, a language spoken in Senegal, Gambia, and Mauritania * The Wolof or Jolof Empire, a medieval West African successor of the Mal ...

also use biquinary systems. For example, the Fula word for 6, ''jowi e go'o'', literally means ''five lusone''.

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

use a symbolic, rather than positional, bi-quinary base, even though

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

is completely decimal.

Examples

Several different representations of bi-quinary coded decimal have been used by different machines. The two-state component is encoded as one or two

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

s, and the five-state component is encoded using three to five bits. Some examples are: * Roman and Chinese

es * Stibitz relay calculators at Bell Labs from Model II onwards *

FACOM 128 The FACOM 128 was a relay-based electromechanical computer built by Fujitsu. Two models were made, namely the FACOM 128A, built in 1956, and the FACOM 128B, built in 1959. , a fully working FACOM 128B is still in working order, maintained by Fujits ...

relay calculators at

Fujitsu is a Japanese multinational information and communications technology equipment and services corporation, established in 1935 and headquartered in Tokyo. Fujitsu is the world's sixth-largest IT services provider by annual revenue, and the la ...

IBM 650 The IBM 650 Magnetic Drum Data-Processing Machine is an early digital computer produced by IBM in the mid-1950s. It was the first mass produced computer in the world. Almost 2,000 systems were produced, the last in 1962, and it was the first ...

– 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) * 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) *

UNIVAC Solid State The UNIVAC Solid State was a magnetic drum-based solid-state computer announced by Sperry Rand in December 1958 as a response to the IBM 650. It was one of the first computers to be (nearly) entirely solid-state, using 700 transistors, and 3000 m ...

– four bits :One ''bi'' bit: 5, three binary coded ''quinary'' bits: 4 2 1 and one parity check bit *

UNIVAC LARC The UNIVAC LARC, short for the ''Livermore Advanced Research Computer'', is a mainframe computer designed to a requirement published by Edward Teller in order to run hydrodynamic simulations for nuclear weapon design. It was one of the earliest s ...

– four bits :One ''bi'' bit: 5, three

Johnson counter A ring counter is a type of counter composed of flip-flops connected into a shift register, with the output of the last flip-flop fed to the input of the first, making a "circular" or "ring" structure. There are two types of ring counters: * A s ...

-coded ''quinary'' bits and one parity check bit

Examples

See also

References

Further reading