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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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- 01011011010
- 01011011011
- 01011011101
- 01011011100
- 01011011010
Correct Option: C
The given generator polynomial (LRC)
G(X) = X3 + X + 1
⇒ 1.X3 + 0.X2 + 1.X1 + 1.X0
G(X) ⇒ 1 0 1 1
Given message m(X) = 0 1 0 1 1 0 1 1.
Then
So, the message 01011011 is transmitted as 01011011101. So, option (c) is correct.