A two-out-of-five code is a

constant-weight code In coding theory, a constant-weight code, also called an ''m''-of-''n'' code, is an error detection and correction code where all codewords share the same Hamming weight. The one-hot code and the balanced code are two widely used kinds of constan ...

that provides exactly ten possible combinations of two bits, and is thus used for representing the

decimal digit A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ...

s using five

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

s. Each bit is assigned a weight, such that the set bits sum to the desired value, with an exception for zero. According to

Federal Standard 1037C Federal Standard 1037C, titled Telecommunications: Glossary of Telecommunication Terms, is a United States Federal Standard issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, a ...

: * each decimal digit is represented by a binary numeral consisting of five bits of which two are of one kind, called ''ones'', and three are of the other kind, called ''zeros'', and * the usual weights assigned to the bit positions are 0-1-2-3-6. However, in this scheme,

zero 0 (zero) is a number representing an empty quantity. In place-value notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or ...

is encoded as binary ''01100''; strictly speaking the 0-1-2-3-6 previously claimed is just a

mnemonic A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imag ...

device. The weights give a unique encoding for most digits, but allow two encodings for 3: 0+3 or 10010 and 1+2 or 01100. The former is used to encode the digit 3, and the latter is used to represent the otherwise unrepresentable zero. The

IBM 7070 IBM 7070 was a decimal-architecture intermediate data-processing system that was introduced by IBM in 1958. It was part of the IBM 700/7000 series, and was based on discrete transistors rather than the vacuum tubes of the 1950s. It was the compa ...

, IBM 7072, and IBM 7074 computers used this code to represent each of the ten decimal digits in a machine word, although they numbered the bit positions 0-1-2-3-4, rather than with weights. Each word also had a sign flag, encoded using a two-out-of-three code, that could be A Alphanumeric, − Minus, or + Plus. When copied to a digit, the three bits were placed in bit positions 0-3-4. (Thus producing the numeric values 3, 6 and 9, respectively.) A variant is the

United States Postal Service The United States Postal Service (USPS), also known as the Post Office, U.S. Mail, or Postal Service, is an independent agency of the executive branch of the United States federal government responsible for providing postal service in the U ...

POSTNET POSTNET (Postal Numeric Encoding Technique) is a barcode symbology used by the United States Postal Service to assist in directing mail. The ZIP Code or ZIP+4 code is encoded in half- and full-height bars. Most often, the delivery point is add ...

barcode A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths, spacings and sizes of parallel lines. These barcodes, now commonly referred to as linear or o ...

, used to represent the ZIP Code for automated mail sorting and routing equipment. This uses two tall bars as ones and three short bars as zeros. Here, the weights assigned to the bit positions are 7-4-2-1-0. Again, zero is encoded specially, using the 7+4 combination (binary 11000) that would naturally encode 11. This method was also used in North American telephone

multi-frequency In telephony, multi-frequency signaling (MF) is a type of signaling that was introduced by the Bell System after World War II. It uses a combination of audible tones for address (telephone number) transport and supervision signaling on trunk lines b ...

and

crossbar switch In electronics and telecommunications, a crossbar switch (cross-point switch, matrix switch) is a collection of switches arranged in a matrix configuration. A crossbar switch has multiple input and output lines that form a crossed pattern of int ...

ing systems. The USPS

Postal Alpha Numeric Encoding Technique The Postal Alpha Numeric Encoding Technique (PLANET) barcode was used by the United States Postal Service to identify and track pieces of mail during delivery - the Post Office's "CONFIRM" services. It was fully superseded by Intelligent Mail Ba ...

(PLANET) uses the same weights, but with the opposite bar-height convention. The

Code 39 Code 39 (also known as Alpha39, Code 3 of 9, Code 3/9, Type 39, USS Code 39, or USD-3) is a variable length, discrete barcode symbology. The Code 39 specification defines 43 characters, consisting of uppercase letters (A through Z), numeric digi ...

barcode uses weights 1-2-4-7-0 (i.e. LSB first,

Parity bit A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes) ...

last) for the widths of its bars, but it also encodes two bits of extra information in the spacing between bars. The , , , , , spacing is used for digits. The following table represents

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

digits from 0 to 9 in various two-out-of-five code systems: The limit on the number of bits set is similar to, but strictly stronger than, a

parity check A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes), ...

. All

s, including the two-out-of-five code, can not only detect any single-bit error, but also detect any

unidirectional error In telecommunication, a Berger code is a unidirectional error detecting code, named after its inventor, J. M. Berger. Berger codes can detect all unidirectional errors. Unidirectional errors are errors that only flip ones into zeroes or only zeroes ...

s -- any case where all errors in a codeword are of a single type (0→1 or 1→0).

References

{{Barcodes Barcodes Computer arithmetic Telephony signals

See also

References