GATE EC 2024 Set 1 — Question 47
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Communications → Error Control Coding → Parity Checks & CRC
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Question
The information bit sequence is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is . The encoded sequence of bits is ________.
Correct answer
(A) \1 1 1 0 1 0 1 0 1 1 1 0 0\
Solution
CRC-4 with (divisor bits ).
(each step slides the 5-bit window one position, bringing down the next bit; XOR with ). The last 4 bits give the remainder is . Check: is exactly divisible by (remainder 0).
1.Append 4 zeros to the message: .
2.Divide by using modulo-2 (XOR) long division:
| Step | Current bits | XOR with | Result |
|---|---|---|---|
| 1 | 11101 | 10011 | 01110 |
| 2 | 11100 | 10011 | 01111 |
| 3 | 11111 | 10011 | 01100 |
| 4 | 11000 | 10011 | 01011 |
| 5 | 10111 | 10011 | 00100 |
| 6 | 01000 | 00000 | 01000 |
| 7 | 10000 | 10011 | 00011 |
| 8 | 00110 | 00000 | 00110 |
| 9 | 01100 | 00000 | 01100 |
3.Encoded word = message followed by the remainder: .
Options B, C, D append , , , which leave a non-zero remainder.Answer: (A)Continue learning with Success Tracker
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