# Q4(a) · CRC codeword

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/papers/paper-2024-ai-final/q4a

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/papers/paper-2024-ai-final--q4a/

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.