Computer Networks · TEE · papers
Q2(b) · CRC encoding
2023-11-22 · AI-only Sem V variant; incomplete recovered scan
Exact historical variant. Current-syllabus questions solved; excluded topics and source limitations stated.
Q2(b). Given message 1011011010 and generator G(x) = x³ + x + 1, calculate the CRC code and transmission message. [5 marks]
Answer
Given
Data = 1011011010; 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
1011011010 → 1011011010000
Step 2. Perform XOR division
| Leading position | Before XOR | Aligned generator | After XOR |
|---|---|---|---|
| 1 | 1011011010000 | 1011000000000 | 0000011010000 |
| 6 | 0000011010000 | 0000010110000 | 0000001100000 |
| 7 | 0000001100000 | 0000001011000 | 0000000111000 |
| 8 | 0000000111000 | 0000000101100 | 0000000010100 |
| 9 | 0000000010100 | 0000000010110 | 0000000000010 |
Step 3. Build the frame
Remainder = 010. Transmit 1011011010010.
Step 4. Divide the received frame
| Position | Before | Generator | After |
|---|---|---|---|
| 1 | 1011011010010 | 1011000000000 | 0000011010010 |
| 6 | 0000011010010 | 0000010110000 | 0000001100010 |
| 7 | 0000001100010 | 0000001011000 | 0000000111010 |
| 8 | 0000000111010 | 0000000101100 | 0000000010110 |
| 9 | 0000000010110 | 0000000010110 | 0000000000000 |
Receiver remainder = 000. No error is detected; this is not a guarantee that every possible corruption is detectable.