Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, notably 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).
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.)
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:
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.
Value | 05-01234 bits [1] | |
---|---|---|
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 |
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.
Value | 1357-9 bits |
---|---|
0 | 0000-0 |
1 | 1000-0 |
2 | 1000-1 |
3 | 0100-0 |
4 | 0100-1 |
5 | 0010-0 |
6 | 0010-1 |
7 | 0001-0 |
8 | 0001-1 |
9 | 0000-1 |
The UNIVAC Solid State uses four bits: one bi bit (5), three binary coded quinary bits (4 2 1) [4] [5] [6] [7] [8] [9] and one 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 |
The UNIVAC LARC has four bits: [9] one bi bit (5), three Johnson counter-coded quinary bits and one 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 |
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications.
A two-out-of-five code is a constant-weight code that provides exactly ten possible combinations of two bits, and is thus used for representing the decimal digits using five bits. Each bit is assigned a weight, such that the set bits sum to the desired value, with an exception for zero.
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit.
A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits can represent any of 256 possible values and can, therefore, represent a wide variety of different items.
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two.
Excess-3, 3-excess or 10-excess-3 binary code, shifted binary or Stibitz code is a self-complementary binary-coded decimal (BCD) code and numeral system. It is a biased representation. Excess-3 code was used on some older computers as well as in cash registers and hand-held portable electronic calculators of the 1970s, among other uses.
Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five digits on either hand.
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Chisanbop or chisenbop, sometimes called Fingermath, is a finger counting method used to perform basic mathematical operations. According to The Complete Book of Chisanbop by Hang Young Pai, chisanbop was created in the 1940s in Korea by Sung Jin Pai and revised by his son Hang Young Pai, who brought the system to the United States in 1977.
Chen–Ho encoding is a memory-efficient alternate system of binary encoding for decimal digits.
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.
A reed relay is a type of relay that uses an electromagnet to control one or more reed switches. The contacts are of magnetic material and the electromagnet acts directly on them without requiring an armature to move them. Sealed in a long, narrow glass tube, the contacts are protected from corrosion. The glass envelope may contain multiple reed switches or multiple reed switches can be inserted into a single bobbin and actuate simultaneously. Reed switches have been manufactured since the 1930s.
A six-bit character code is a character encoding designed for use on computers with word lengths a multiple of 6. Six bits can only encode 64 distinct characters, so these codes generally include only the upper-case letters, the numerals, some punctuation characters, and sometimes control characters. The 7-track magnetic tape format was developed to store data in such codes, along with an additional parity bit.
Gillham code is a zero-padded 12-bit binary code using a parallel nine- to eleven-wire interface, the Gillham interface, that is used to transmit uncorrected barometric altitude between an encoding altimeter or analog air data computer and a digital transponder. It is a modified form of a Gray code and is sometimes referred to simply as a "Gray code" in avionics literature.
A decimal computer is a computer that can represent numbers and addresses in decimal and that provides instructions to operate on those numbers and addresses directly in decimal, without conversion to a pure binary representation. Some also had a variable wordlength, which enabled operations on numbers with a large number of digits.
In digital computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure information contained in messages and the entropy of random variables.
Offset binary, also referred to as excess-K, excess-N, excess-e, excess code or biased representation, is a method for signed number representation where a signed number n is represented by the bit pattern corresponding to the unsigned number n+K, K being the biasing value or offset. There is no standard for offset binary, but most often the K for an n-bit binary word is K = 2n−1 (for example, the offset for a four-digit binary number would be 23=8). This has the consequence that the minimal negative value is represented by all-zeros, the "zero" value is represented by a 1 in the most significant bit and zero in all other bits, and the maximal positive value is represented by all-ones (conveniently, this is the same as using two's complement but with the most significant bit inverted). It also has the consequence that in a logical comparison operation, one gets the same result as with a true form numerical comparison operation, whereas, in two's complement notation a logical comparison will agree with true form numerical comparison operation if and only if the numbers being compared have the same sign. Otherwise the sense of the comparison will be inverted, with all negative values being taken as being larger than all positive values.
BCD, also called alphanumeric BCD, alphameric BCD, BCD Interchange Code, or BCDIC, is a family of representations of numerals, uppercase Latin letters, and some special and control characters as six-bit character codes.
The Aiken code is a complementary binary-coded decimal (BCD) code. A group of four bits is assigned to the decimal digits from 0 to 9 according to the following table. The code was developed by Howard Hathaway Aiken and is still used today in digital clocks, pocket calculators and similar devices.
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. As of 2019, a fully working FACOM 128B is still in working order, maintained by Fujitsu staff at a facility in Numazu in Shizuoka Prefecture.
[…] The use of the biquinary code in this respect is typical. The binary part (i.e., the most significant bit) and the quinary part (the other 4 bits) are first added separately; then the quinary carry is added to the binary part. If a binary carry is generated, this is propagated to the quinary part of the next decimal digit to the left. […](xxiv+835+1 pages)
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