Discussion
Consider the transmission of data bits 110001011 over a link that uses Cyclic Redundancy Check (CRC) code for error detection. If the generator bit pattern is given to be 1001, which one of the following options shows the remainder bit pattern appended to the data bits before transmission?
Answer: D
The remainder appended is 100.
The generator 1001 has degree 3, so append three zeros to the data, 110001011 000, and divide by 1001 using modulo-2 (XOR) arithmetic. Each step XORs 1001 under the leading 1:
110001011000
1001
010101011000
1001
000111011000
1001
000011111000
1001
000001101000
1001
000000100000
1001
000000000100
The last three bits, 100, are the remainder, and the transmitted frame is 110001011100. A check: that frame divided by 1001 leaves remainder 000.
000 would mean the data were already a multiple of the generator, and 011 and 101 come from slips in the XOR steps.
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