In CRC coding, the data word is 111111, the divisor is 1010, and the remainder…
2022
In CRC coding, the data word is 111111, the divisor is 1010, and the remainder is 110. Which of the following is the valid codeword?
Answer: C. 111111110 — Concept: A CRC generator with four bits has degree 3, so its remainder contains three bits. The transmitted codeword is formed by appending that remainder to…
- A.
011111101
- B.
001010110
- C.
111111110
- D.
110111111
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Show answer & explanation
Correct answer: C
Concept: A CRC generator with four bits has degree 3, so its remainder contains three bits. The transmitted codeword is formed by appending that remainder to the original data word; a correct codeword is divisible by the generator under modulo-2 (XOR) division.
Application:
Append three zeros to the six-bit data word to form the dividend 111111000.
Divide 111111000 by 1010 using modulo-2 XOR division. The remainder is 110, as stated in the question.
Append the three-bit remainder to the unchanged data word: 111111 followed by 110 gives 111111110.
Cross-check: Modulo-2 division of 111111110 by 1010 leaves 000. The zero residual confirms that the constructed nine-bit sequence is a valid CRC codeword.
Result: The valid codeword is 111111110.
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