4 (**). Richard Hamming in 1950 produced an innovative way to improve the string parity error- checking process to ensure data is accurately and reliably transmitted. Parity is often referred to as ODD or EVEN, by adding up the bit values in a string. If EVEN parity is used, the string 10110101, which has 5 bits, is appended with the value 1 to make the total number of bits even. If ODD parity is used, the same string would be appended with a 0, to maintain an odd total for all the bits, resulting in 101101010 as the transmitted string. Hamming's work produced not only a way to check if there is an error, but when the error is in the string. For a bit string of length 8, which is 2^3, 4 bits can be added to create Hammin parity string. For a string of 2^N bits, the leftmost bit is considered position 1 and the rightmost bit is position 2^N. The parity bits will be placed at each position that is a power of 2 (i.e., at positions 1, 2, 4, 8, 16, ...), with the actual data bits starting in position 3, then 5, 6, 7, 9, 10, ... and so on. For the string 10110101, which can be represented by the hex string B5, the Hammond parity string would start out a 1 2 3 4 5 6 7 8 9 10 11 12 __1_0 1 1 0 1 0 1
4 (**). Richard Hamming in 1950 produced an innovative way to improve the string parity error- checking process to ensure data is accurately and reliably transmitted. Parity is often referred to as ODD or EVEN, by adding up the bit values in a string. If EVEN parity is used, the string 10110101, which has 5 bits, is appended with the value 1 to make the total number of bits even. If ODD parity is used, the same string would be appended with a 0, to maintain an odd total for all the bits, resulting in 101101010 as the transmitted string. Hamming's work produced not only a way to check if there is an error, but when the error is in the string. For a bit string of length 8, which is 2^3, 4 bits can be added to create Hammin parity string. For a string of 2^N bits, the leftmost bit is considered position 1 and the rightmost bit is position 2^N. The parity bits will be placed at each position that is a power of 2 (i.e., at positions 1, 2, 4, 8, 16, ...), with the actual data bits starting in position 3, then 5, 6, 7, 9, 10, ... and so on. For the string 10110101, which can be represented by the hex string B5, the Hammond parity string would start out a 1 2 3 4 5 6 7 8 9 10 11 12 __1_0 1 1 0 1 0 1
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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