Bi-quinary coded decimal
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Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, including 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 abaci, one bead indicating 0..4 or 5..9 and 4 beads indicating which of those ranges.
[edit] Decoding
To decode the Biquinary code use the number 5043210.
At each digit multiple the biquinary number times the number 5043210. This will give you the decimal number.
For example take the number 0110000. To change this into Decimal:
(5 * 0) + (0 * 1) + (4 * 1) + (3 * 0) + (2 * 0) + (1 * 0) + (0 * 0) = 4
[edit] 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:
- IBM 650 – 7 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 set in a valid digit); in the picture of the front panel below, the bi-quinary encoding of the internal workings of the machine are evident in the arrangement of the lights (active bits are just visible)
| Value | 05-01234 Bits | 
|
| 0 | 10-10000 | |
| 1 | 10-01000 | |
| 2 | 10-00100 | |
| 3 | 10-00010 | |
| 4 | 10-00001 | |
| 5 | 01-10000 | |
| 6 | 01-01000 | |
| 7 | 01-00100 | |
| 8 | 01-00010 | |
| 9 | 01-00001 |
- UNIVAC 60 and UNIVAC 120 – 5 bits (four ‘quinary’ bits: 1 3 5 7 and one ‘bi’ bit: 9)
| Value | 13579 bits |
| 0 | 00000 |
| 1 | 10000 |
| 2 | 10001 |
| 3 | 01000 |
| 4 | 01001 |
| 5 | 00100 |
| 6 | 00101 |
| 7 | 00010 |
| 8 | 00011 |
| 9 | 00001 |
- UNIVAC Solid State – 4 bits (one ‘bi’ bit: 5 and three binary coded ‘quinary’ bits: 4 2 1) with 1 parity check bit
| Value | p-5-421 bits |
| 0 | 1-0-000 |
| 1 | 0-0-001 |
| 2 | 0-0-010 |
| 3 | 1-0-011 |
| 4 | 0-0-100 |
| 5 | 0-1-000 |
| 6 | 1-1-001 |
| 7 | 1-1-010 |
| 8 | 0-1-011 |
| 9 | 1-1-100 |
- Univac LARC – 4 bits (one ‘bi’ bit: 5 and three ring counter coded ‘quinary’ bits) with 1 parity check bit
| Value | p-5-qqq bits |
| 0 | 1-0-000 |
| 1 | 0-0-001 |
| 2 | 1-0-011 |
| 3 | 0-0-111 |
| 4 | 1-0-110 |
| 5 | 0-1-000 |
| 6 | 1-1-001 |
| 7 | 0-1-011 |
| 8 | 1-1-111 |
| 9 | 0-1-110 |
