The Hamming(7,4) Code

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Hamming(7,4) is a single-error correcting code that uses a 7-bit codeword to transmit four bits of data. The sender computes three parity bits for each 4-bit data word, assembles the data and parity bits into a 7-bit codeword, and transmits this codeword. The receiver computes three parity check bits from the received 7-bit word. If no error occurred in transmission, all three parity check bits will be zero. If a single bit has been changed in transmission, the value of the three parity bits (interpreted as a 3-bit binary number) will indicate the position of the error, which can then be corrected.

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This Demonstration allows you to simulate such a transmission by setting the data bits to be transmitted at the top, and introducing an error, if desired, in any position of the transmitted word.

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Contributed by: Jacob A. Siehler (March 2011)
Open content licensed under CC BY-NC-SA


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