GATE 2017 CS – Question 42
A computer network uses polynomials over GF(2) for error checking with 8 bits as information bits and uses $x^3 + x + 1$ as the generator polynomial to generate the check bits. In this network, the message 01011011 is transmitted as
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Correct answer: (C) 01011011101
Explanation
The generator $x^3 + x + 1$ is 1011. Append three zeros to the message to get 01011011000, and divide by 1011 using exclusive-OR. Dividing 1011011000 by 1011 step by step leaves the remainder 101. Replacing the three zeros with the remainder gives the transmitted message 01011011101.