Two-out-of-five code

In telecommunication, a two-out-of-five code is an m of n code that provides exactly ten possible combinations, and thus is popular for representing decimal digits using five binary bits. An m of n code is a separable Error detection code with a code word length of n bits where each code word contains exactly m instances There are ways to assign weights to each bit such that the set bits sum to the desired value, with an exception for zero.

According to Federal Standard 1037C:

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. Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration In Mathematics and Computer science, a digit is a symbol (a number symbol e However, in this scheme, zero is encoded as "binary" 01100; strictly speaking the 0-1-2-3-6 previously claimed is just a mnemonic device. A mnemonic device (nəˈmɒnɪk is a Memory aid Commonly met mnemonics are often verbal something such as a very short poem or a special word used to help a person remember

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 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. IBM 7070 was a decimal architecture intermediate data processing system that was introduced by IBM in June 1960 The IBM 700/7000 series was a series of large scale ( mainframe) Computer systems made by IBM through The IBM 700/7000 series was a series of large scale ( mainframe) Computer systems made by IBM through 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.

A variant is the U.S. Post Office POSTNET barcode, used to represent the ZIP+4 code for automated mail sorting and routing equipment. Example The above-mentioned example of 55555-1237 yields Sum is 38 The check digit is therefore 2 The data encoded will A bar code (also barcode) is an optical Machine-readable representation of data The ZIP code is the system of Postal codes used by the United States Postal Service (USPS 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 and crossbar switching systems. In Telephony Multi-Frequency (MF is an outdated in-band signaling technique A crossbar switch (also known as cross-point switch, crosspoint switch, or matrix switch) is a Switch connecting multiple inputs to multiple [1]

The following table represents decimal digits from 0 to 9 in various two-out-of-five code systems:

Digit	Telecommunication 01236	IBM 7070, 7072, 7074 01234	POSTNET 74210
0	01100	01100	11000
1	11000	11000	00011
2	10100	10100	00101
3	10010	10010	00110
4	01010	01010	01001
5	00110	00110	01010
6	10001	10001	01100
7	01001	01001	10001
8	00101	00101	10010
9	00011	00011	10100
A	N/A	1––10	N/A
−	N/A	1––01	N/A
+	N/A	0––11	N/A

The decimal ( base ten or occasionally denary) Numeral system has ten as its base.

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