Surf Wiki
Save to docs
general/computer-arithmetic

From Surf Wiki (app.surf) — the open knowledge base

Bi-quinary coded decimal

Numeral encoding scheme

Bi-quinary coded decimal
Summary

Numeral encoding scheme

2-out-of-7

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 encoding scheme used in many abacuses and in some early computers, notably the Colossus. The term bi-quinary indicates that the code comprises both a two-state (bi) and a five-state (quinary) 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 and 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.

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 two 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 mechanical relays.)

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

  • Roman and Chinese abacuses
  • Stibitz relay calculators at Bell Labs from Model II onwards
  • FACOM 128 relay calculators at Fujitsu

IBM 650

IBM650code The IBM 650 uses seven bits: two bi bits (0 and 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. The bi-quinary encoding of the internal workings of the machine are evident in the arrangement of its lights – the bi bits form the top of a T for each digit, and the quinary bits form the vertical stem.

Value05-01234 bits
[[File:IBM-650-panel.jpgthumbcenterIBM 650 front panel while running, with active bits just discernible]]
0
1
2
3
4
5
6
7
8
9

Remington Rand 409

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.

Value1357-9 bits
0
1
2
3
4
5
6
7
8
9

UNIVAC Solid State

The UNIVAC Solid State uses four bits: one bi bit (5), three binary coded quinary bits (4 2 1) and one parity check bit

Valuep-5-421 bits
0
1
2
3
4
5
6
7
8
9

UNIVAC LARC

The UNIVAC LARC has four bits: one bi bit (5), three Johnson counter-coded quinary bits and one parity check bit.

Valuep-5-qqq bits
0
1
2
3
4
5
6
7
8
9

References

References

  1. (2015-12-04). "Why Use Binary? - Computerphile". YouTube.
  2. (1962). "Taschenbuch der Nachrichtenverarbeitung". [[Springer-Verlag OHG]].
  3. (1967). "Taschenbuch der Nachrichtenverarbeitung". [[Springer-Verlag OHG]].
  4. (1974). "Taschenbuch der Informatik - Band II - Struktur und Programmierung von EDV-Systemen". [[Springer-Verlag]].
  5. (1973-06-18). "Digital Electronics". [[The Macmillan Press Ltd.]] / [[N. V. Philips' Gloeilampenfabrieken]].
  6. (1975). "Digitale Elektronik in der Meßtechnik und Datenverarbeitung: Theoretische Grundlagen und Schaltungstechnik". [[Deutsche Philips GmbH]].
  7. (1957). "Mathematics and Computers". [[McGraw-Hill Book Company, Inc.]].
  8. (2018). "Decimal Representations". quadibloc.
  9. (1960). "Digital Computer and Control Engineering". [[McGraw-Hill Book Company, Inc.]] (printer: The Maple Press Company, York, Pennsylvania, US).
  10. (1991-09-30). "Military Handbook: Encoders - Shaft Angle To Digital". [[United States Department of Defense]].
Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

computer-arithmetic numeral-systems
Want to explore this topic further?

Ask Mako anything about Bi-quinary coded decimal — get instant answers, deeper analysis, and related topics.

Research with Mako

Free with your Surf account

Content sourced from Wikipedia, available under CC BY-SA 4.0.

This content may have been generated or modified by AI. CloudSurf Software LLC is not responsible for the accuracy, completeness, or reliability of AI-generated content. Always verify important information from primary sources.

Report