The message 11001001 is to be transmitted using the CRC polynomial x3 + 1 to…

2007

The message 11001001 is to be transmitted using the CRC polynomial x3 + 1 to protect it from errors. The message that should be transmitted is:

  1. A.

    11001001000

  2. B.

    11001001011

  3. C.

    11001010

  4. D.

    110010010011

Attempted by 149 students.

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Correct answer: B

Solution: compute the 3-bit CRC and form the transmitted message.

Generator polynomial: x^3 + 1 → generator bits 1001 (degree 3).

  1. Append three zeros (degree of generator) to the 8-bit message: 11001001 → 11001001000.

  2. Divide 11001001000 by the generator 1001 using modulo-2 (XOR) division. Performing the binary division yields a remainder of 011.

  3. Append the 3-bit remainder 011 to the original 8-bit message: 11001001 + 011 = 11001001011.

Check: dividing the transmitted word 11001001011 by 1001 gives remainder 000, confirming the transmitted message is correct.

Final transmitted message: 11001001011

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