In CRC checksum method, assume that given frame for transmission is 1101011011…
2016
In CRC checksum method, assume that given frame for transmission is 1101011011 and the generator polynomial is \(G(x) = x^{4}+ x + 1\).
After implementing CRC encoder, the encoded word sent from sender side is _____.
- A.
11010110111110
- B.
11101101011011
- C.
110101111100111
- D.
110101111001111
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Correct answer: A
Solution: Compute the 4-bit CRC for the 10-bit frame using generator polynomial G(x) = x^4 + x + 1 (divisor 10011).
Step 1: Convert the generator to binary and determine its degree. G(x) = x^4 + x + 1 corresponds to divisor 10011 and has degree 4, so append four zeros to the frame.
Step 2: Append four zeros to the 10-bit frame 1101011011 to get 11010110110000, then divide this padded bitstring by 10011 using binary (XOR) division. Perform XOR subtraction whenever the current leftmost bit is 1.
Step 3: After completing the binary division the 4-bit remainder is 1110.
Step 4: Append the remainder to the original frame: 1101011011 + 1110 = 11010110111110. This is the encoded word sent by the sender.
Verification: Dividing the encoded word 11010110111110 by 10011 yields a zero remainder (0000), confirming the CRC is correct.