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GATE CSE 2026 Session 2 Q43: CRC remainder for data 110001011 with generator 1001

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?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: D (official GATE 2026 final answer key)

Concept used: CRC: append (degree of generator) zeros and take the modulo-2 remainder.

First step: The generator has 4 bits, so append three zeros: divide 110001011000 by 1001 using XOR long division.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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