# Q6(b) · CRC

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/papers/paper-2025-feb-reexam/q6b

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/papers/paper-2025-feb-reexam--q6b/

Actual paper; 100 marks attempted. Current-syllabus alignment is stated per question.

### Q6(b). Given the data bit sequence 1010011110 and the CRC polynomial of x^3+x+1. Determine the transmitted message from the sender. Illustrate the process of checking the received message for any errors at the receiver side. [10 marks]

### Answer

### Given

Data = 1010011110; 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

1010011110 → 1010011110000

### Step 2. Perform XOR division

| Leading position | Before XOR | Aligned generator | After XOR |
| --- | --- | --- | --- |
| 1 | 1010011110000 | 1011000000000 | 0001011110000 |
| 4 | 0001011110000 | 0001011000000 | 0000000110000 |
| 8 | 0000000110000 | 0000000101100 | 0000000011100 |
| 9 | 0000000011100 | 0000000010110 | 0000000001010 |
| 10 | 0000000001010 | 0000000001011 | 0000000000001 |

### Step 3. Build the frame

Remainder = **001**. Transmit **1010011110001**.

### Step 4. Divide the received frame

| Position | Before | Generator | After |
| --- | --- | --- | --- |
| 1 | 1010011110001 | 1011000000000 | 0001011110001 |
| 4 | 0001011110001 | 0001011000000 | 0000000110001 |
| 8 | 0000000110001 | 0000000101100 | 0000000011101 |
| 9 | 0000000011101 | 0000000010110 | 0000000001011 |
| 10 | 0000000001011 | 0000000001011 | 0000000000000 |

Receiver remainder = 000. No error is detected; this is not a guarantee that every possible corruption is detectable.