Discussion
If the frame to be transmitted is 1101011011 and the CRC polynomial to be used for generating checksum is \(x^{4} + x + 1\), then what is the transmitted frame ?
Answer: A
The transmitted frame is 11010110111110.
The generator \(x^{4} + x + 1\) is the bit pattern 10011, of degree 4. Append four 0s to the frame and divide by 10011 using modulo-2 (XOR) division:
\[ \begin{aligned} &11010110110000 \div 10011 \\ &\text{remainder} = 1110 \end{aligned} \]
Replacing the four appended 0s with the remainder gives the transmitted frame 1101011011 1110. The receiver divides it by 10011 and gets remainder 0 if no error occurred.
The other options keep the original frame but attach the wrong check bits (1011, 1101 or 1001), so their division by 10011 would not leave remainder 0.
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