Discussion
The message 11001001 is to be transmitted using the CRC polynomial \(x^{3} + 1\) to protect it from errors. The message that should be transmitted is
Answer: D
The transmitted message is 11001001011. The generator \(x^{3} + 1\) is 1001, of degree 3, so three zeros are appended to the message, giving 11001001000. Dividing by 1001 using modulo-2 arithmetic leaves the remainder 011.
\[ 11001001000 \div 1001 \Rightarrow \text{remainder } 011 \]
The remainder is placed in the place of the appended zeros, so the frame is 11001001011. Option B is the unprotected message and options A and C do not have 3 check bits appended.
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