GATE CS 2026 Set 2 — Question 43
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Computer Networks → Data Link Layer → Error Detection (Parity, CRC)
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Question
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?
Correct answer
(D) 100
Solution
To find the CRC remainder, we perform binary division (modulo-2 arithmetic) of the data bits appended with zeros by the generator polynomial, where is the number of bits in the generator.Data:
Generator: (4 bits, so append 3 zeros)
Dividend: Performing the division:
The remainder is .
Generator: (4 bits, so append 3 zeros)
Dividend: Performing the division:
110001011
_____________
1001 ) 110001011000
1001
----
1010
1001
----
0111
0000
----
1110
1001
----
1111
1001
----
1101
1001
----
1000
1001
----
0010
0000
----
0100
0000
----
100
The remainder is .
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