Computer Networks · TEE · papers
Q2(b)(ii) · CRC and syndrome
2023-01-27 · AI-only Sem V
Exact historical variant. Current-syllabus questions solved; excluded topics and source limitations stated.
Q2(b)(ii). Data 1001 is transmitted using G(x)=x³+x+1. (a) Find the transmitted codeword. (b) Explain the role of syndrome bits at the receiver. [5 marks]
Answer
Given
Data = 1001; generator bits = 1011; 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
1001 → 1001000
Step 2. Perform XOR division
| Leading position | Before XOR | Aligned generator | After XOR |
|---|---|---|---|
| 1 | 1001000 | 1011000 | 0010000 |
| 3 | 0010000 | 0010110 | 0000110 |
Step 3. Build the frame
Remainder = 110. Transmit 1001110.
Step 4. Divide the received frame
| Position | Before | Generator | After |
|---|---|---|---|
| 1 | 1001110 | 1011000 | 0010110 |
| 3 | 0010110 | 0010110 | 0000000 |
Receiver remainder = 000. No error is detected; this is not a guarantee that every possible corruption is detectable.