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:
- A.
11001001000
- B.
11001001011
- C.
11001010
- 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).
Append three zeros (degree of generator) to the 8-bit message: 11001001 → 11001001000.
Divide 11001001000 by the generator 1001 using modulo-2 (XOR) division. Performing the binary division yields a remainder of 011.
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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