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Hamming Code

Hamming code is one of the error-correcting codes that most commonly used in RAMS. In this code, k parity bits are added to n-bit data word to form a new word n + k bits, bit positions are numbered in sequence from 1 to n + k. Their positions numbered as a power of 2 which provided for parity bits, the bits of the rest is bits of data. The code can be used with the words of any length. For example, 8 bits data word 11000100. We include 4 parity bits with the 8-bit data word arrange 12 bit set as follows:

The 4 parity bits, P1, P2, P4 and P8, are in positions 1, 2, 4, and 8, respectively. The 8 bits of the data word are in the remaining position. Each parity bit is calculated as follows:
P1 = XOR of bits (3, 5, 7, 9, 11)
P2 = XOR of bits (3, 6, 7, 10, 11)
P4 = XOR of bits (5, 6, 7, 12)
P8 = XOR of bits (9, 10, 11, 12)

Then the stored 8-bit word data is (together with 4 parity bits)

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