Hamming(7,4)

Hamming(7,4) is a Hamming code that encodes 4 bits of data into 7 bits by adding 3 parity bits.

Today, Hamming code really refers to a specific (7,4) code Richard W. Hamming introduced in 1950. The code stemmed from his work as a theorist at Bell Telephone laboratories in the 1940s. Hamming invented the code in 1950 to provide a error-correcting code to reduce value computer resources / time being wasted. [cite web | url = http://biobio.loc.edu/chu/web/Courses/Cosi460/hamming_codes.htm | title = History of Hamming Codes | accessdate = 2008-04-03]

Hamming Code adds three additional check bits to every four data bits of the message. Hamming's (7,4) algorithm can correct any single-bit error, or detect all single-bit and two-bit errors. This means that for transmission medium situations where burst errors do not occur, Hamming's (7,4) code is effective (as the medium would have to be extremely noisy for 2 out of 7 bits to be flipped).In other words, the Hamming distance between the transmitted and received words must be no greater than one to be correctable.

Goal

The goal of Hamming codes is to create a set of parity bits that overlap such that a single-bit error (the bit is logically flipped in value) in a data bit "or" a parity bit can be detected "and" corrected.While multiple overlaps can be created, the general method is presented in Hamming codes.

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