Bi-quinary coded decimal

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Code Biquinaer.svg
Biquinary code example [1]
Code Biquinaer reflektiert.svg
Reflected biquinary code
Japanese abacus. The right side represents 1,234,567,890 in bi-quinary: each column is one digit, with the lower beads representing "ones" and the upper beads "fives". Soroban.JPG
Japanese abacus. The right side represents 1,234,567,890 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, including the Colossus. [2] 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).

Contents

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 2 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:

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)
Value05-01234 bits [1]
IBM 650 front panel IBM-650-panel.jpg
IBM 650 front panel
Close-up of IBM 650 indicators IBM 650 panel close-up of bi-quinary indicators.jpg
Close-up of IBM 650 indicators
010-10000
110-01000
210-00100
310-00010
410-00001
501-10000
601-01000
701-00100
801-00010
901-00001
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)
Value1357-9 bits
00000-0
11000-0
21000-1
30100-0
40100-1
50010-0
60010-1
70001-0
80001-1
90000-1
One bi bit: 5, three binary coded quinary bits: 4 2 1 [4] [5] [6] [7] [8] [9] and one parity check bit
Valuep-5-421 bits
01-0-000
10-0-001
20-0-010
31-0-011
40-0-100
50-1-000
61-1-001
71-1-010
80-1-011
91-1-100
One bi bit: 5, three Johnson counter-coded quinary bits and one parity check bit
Valuep-5-qqq bits
01-0-000
10-0-001
21-0-011
30-0-111
41-0-110
50-1-000
61-1-001
70-1-011
81-1-111
90-1-110

See also

Related Research Articles

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References

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Further reading