The checker at the receiver does the same thing as the generator in the sender with one exception: The addition is done over all 5 bits. The sender sends the code word which may be corrupted during transmission. In other words, If the number of 1s is even, the result is 0 if the number of 1s is odd, the result is 1.In both cases, the total number of 1s in the code word is even. This is normally done by adding the 4 bits of the data word (modulo-2). The parity bit that is added makes the number of 1s in the code word even. The data word bits and the parity bit create the 5-bit code word. The encoder uses a generator that takes a copy of a 4-bit data word (a0, a1, a2 and a3) and generates a parity bit r0. The following figure shows possible structure of an encoder (at the sender) and a decoder (at the receiver). The minimum Hamming distance for this category is dmin =2, which means that the code is a single-bit error-detecting code and it cannot correct any error. Although some implementations specify an odd number of 1s. The extra bit, called the parity bit, is selected to make the total number of 1s in the code word even. In this code, a k-bit data word is changed to an n-bit code word where n = k + 1. The simple parity-check code is the most familiar error-detecting code.
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