Bi-quinary coded decimal is a
numeral encoding schemeA numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
used in many
abacusThe abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abacuses are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets...
es and in some early computers, including the
ColossusThe Colossus machines were electronic computing devices used by British codebreakers to read encrypted German messages during World War II. These were the world's first programmable, digital, electronic, computing devices...
. 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.
Several human languages, most notably
KhmerKhmer , or Cambodian, is the language of the Khmer people and the official language of Cambodia. It is the second most widely spoken Austroasiatic language , with speakers in the tens of millions. Khmer has been considerably influenced by Sanskrit and Pali, especially in the royal and religious...
and
WolofWolof is a language spoken in Senegal, The Gambia, and Mauritania, and is the native language of the ethnic group of the Wolof people. Like the neighboring language Fula, it belongs to the Atlantic branch of the Niger-Congo language family...
, also use biquinary systems. For example, the Khmer word for 6,
pram muoy, literally means
five [plus] one.
To decode the Biquinary code use the number
5043210.
At each digit multiply the biquinary number by the number 5043210.
Discussion
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Bi-quinary coded decimal is a
numeral encoding schemeA numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
used in many
abacusThe abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abacuses are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets...
es and in some early computers, including the
ColossusThe Colossus machines were electronic computing devices used by British codebreakers to read encrypted German messages during World War II. These were the world's first programmable, digital, electronic, computing devices...
. 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.
Several human languages, most notably
KhmerKhmer , or Cambodian, is the language of the Khmer people and the official language of Cambodia. It is the second most widely spoken Austroasiatic language , with speakers in the tens of millions. Khmer has been considerably influenced by Sanskrit and Pali, especially in the royal and religious...
and
WolofWolof is a language spoken in Senegal, The Gambia, and Mauritania, and is the native language of the ethnic group of the Wolof people. Like the neighboring language Fula, it belongs to the Atlantic branch of the Niger-Congo language family...
, also use biquinary systems. For example, the Khmer word for 6,
pram muoy, literally means
five [plus] one.
Decoding
To decode the Biquinary code use the number
5043210.
At each digit multiply the biquinary number by the number 5043210. This will give you the decimal number.
For example take the number 0110000.
To change this into 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
bitIn computing and telecommunications a bit is a basic unit of information storage and communication . It is the maximum amount of information that can be stored by a device or other physical system that can normally exist in only two distinct states...
s, and the five-state component is encoded using three to five bits. Some examples are:
- IBM 650
The IBM 650 was one of IBM’s early computers, and the world’s first mass-produced computer. It was announced in 1953, and over 2000 systems were produced between the first shipment in 1954 and its final manufacture in 1962...
– 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 – 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 just discernible)
| Value |
05-01234 Bits |
IBM 650 front panel |
| 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
The UNIVAC Solid State was a 2-address, bi-quinary coded decimal computer, with memory on a rotating drum with 5000 signed 10 digit words, spinning at 17,667 RPM in a helium atmosphere. It was announced by Sperry Rand in December 1958, as a response to the IBM 650...
– 4 bits (one ‘bi’ bit: 5 and three binary coded ‘quinary’ bits: 4 2 1) with 1 parity check bitA parity bit is a bit that is added to ensure that the number of bits with the value one in a set of bits is even or odd. Parity bits are used as the simplest form of error detecting code....
| 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
A ring counter is a type of counter composed of a circular shift register. The output of the last shift register is fed to the input of the first register.There are two types of ring counters:...
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 |