Hamming is a telecommunications technology term that refers to a family of linear error-correcting codes that make up the Hamming Code invented by Richard Hamming in 1950. Hamming codes can detect up to two and correct up to one bit errors.A PDF with examples of Hamming code and how it works is available from exp.math.uni, located here:
. http://www.exp-math.uni-essen.de/~svaba/Hamming_Code_Project.pdf. A HammingCode can be used to detect and correct a one-bit change in an encoded code word. Thisapproach can be useful as a change in a single bit is more probable than a change in twobits or more bits.The website www.cis.fiu.edu, viewable here, http://users.cis.fiu.edu/~downeyt/cop3402/hamming.html, gives step-by-step instructions for how to calculate this code. The procedure is as follows: 1)Mark all bit positions that are powers of two as parity bits. (positions 1, 2, 4, 8, 16, 32, 64 and so forth) 2) All other bit positions are for the data to be encoded. (positions 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, and so forth) 3) Each parity bit calculates the parity for some of the bits in the code word. The position of the parity bit determines the sequence of bits that it alternately checks and skips.The above example created a code word of 011100101010. Suppose the word that was received was 011100101110 instead. Then the receiver could calculate which bit was wrong and correct it. The method is to verify each check bit. Write down all the incorrect parity bits. This will reveal that parity bits two and eight are incorrect. It is not an accident that 2 + 8 = 10, and that bit position 10 is the location of the bad bit. Check each parity bit, and add the positions that are wrong, this will show the location of the bad bit.More reference links: http://www.exp-math.uni-essen.de/~svaba/Hamming_Code_Project.pdf http://users.cis.fiu.edu/~downeyt/cop3402/hamming.html
