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Q4(a) · CRC codeword
2024-12-06 · AI-only Sem V variant
Exact historical variant. Current-syllabus questions solved; excluded topics and source limitations stated.
Q4(a). Transmit bit stream 10011101 using CRC with G(x)=x³+1. Show the actual transmitted bit string. [5 marks]
Answer
Given
Data = 10011101; generator bits = 1001; degree r = 3.
To find
CRC remainder, complete transmitted frame and receiver check.
Formula and why
Append r zeros, divide using XOR (modulo 2), and replace those zeros with the r-bit remainder. XOR has no borrowing or carrying. A valid received codeword has remainder zero; the receiver does not append new zeros.
Step 1. Append zeros
10011101 → 10011101000
Step 2. Perform XOR division
| Leading position | Before XOR | Aligned generator | After XOR |
|---|---|---|---|
| 1 | 10011101000 | 10010000000 | 00001101000 |
| 5 | 00001101000 | 00001001000 | 00000100000 |
| 6 | 00000100000 | 00000100100 | 00000000100 |
Step 3. Build the frame
Remainder = 100. Transmit 10011101100.
Step 4. Divide the received frame
| Position | Before | Generator | After |
|---|---|---|---|
| 1 | 10011101100 | 10010000000 | 00001101100 |
| 5 | 00001101100 | 00001001000 | 00000100100 |
| 6 | 00000100100 | 00000100100 | 00000000000 |
Receiver remainder = 000. No error is detected; this is not a guarantee that every possible corruption is detectable.