In CRC coding if the data word is 111111, divisor is 1010 and the remainder is…
2022
In CRC coding if the data word is 111111, divisor is 1010 and the remainder is 110. Which of the following code is true?
- A.
011111101
- B.
001010110
- C.
111111110
- D.
110111111
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Correct answer: C
Key idea: For CRC, append r parity bits (the remainder) to the data word, where r is the degree of the divisor polynomial. The divisor 1010 has degree 3, so r = 3.
Step 1: Append three zeros to the data word 111111 to prepare for division: 111111000.
Step 2: Divide 111111000 by the divisor 1010 using modulo-2 (XOR) division. The remainder obtained is 110.
Step 3: Append the remainder 110 to the original data word 111111 to form the codeword 111111110.
Verification: Divide the codeword 111111110 by 1010 using modulo-2 division. The division yields remainder 000, so the codeword is valid (no residual).
Answer: The correct codeword is 111111110.
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