# Q2A · Error detection and correction

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/mocks/tee-mock-b/q2a

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/mocks/tee-mock-b--q2a/

TEE · 100 attempted marks · solutions for every choice · current syllabus 702AI0C023

### TEE practice mock · Q2A. For message bits 101101 and generator 10011, calculate the CRC and transmitted frame. Check the frame at the receiver and show a detected one-bit error. [10 mock marks]

#### Answer

## Given

Message=101101; generator=10011; generator degree r=4. This is textbook systematic CRC with zero initial remainder and no reflection/final XOR.

## To find

Exactly r CRC bits, the transmitted frame and receiver syndromes.

## Formula and why



$$
R=(M\,2^r)\bmod_2 G,\qquad T=(M\,2^r)\oplus R
$$



Modulo-2 division uses aligned XOR, not ordinary decimal division.

## Step-by-step solution

#### Step 1. Preserve all polynomial coefficients

Message bits=101101; generator bits=10011. Leading exponent is 4, so CRC length is 4.

#### Step 2. Append zeros

101101 followed by 4 zeros = 1011010000.

#### Step 3. Perform each nonzero XOR subtraction

| Before | Aligned generator | After XOR |
| --- | --- | --- |
| 1011010000 | 1001100000 | 0010110000 |
| 0010110000 | 0010011000 | 0000101000 |
| 0000101000 | 0000100110 | 0000001110 |

Remainder padded to 4 bits = **1110**. Leading zero columns need no subtraction.

#### Step 4. Construct the transmitted frame

Message + CRC = 101101 + 1110 = **1011011110**.

#### Step 5. Check the full frame

| Before | Aligned generator | After XOR |
| --- | --- | --- |
| 1011011110 | 1001100000 | 0010111110 |
| 0010111110 | 0010011000 | 0000100110 |
| 0000100110 | 0000100110 | 0000000000 |

Receiver remainder = 0000; the uncorrupted frame passes.

#### Step 6. Demonstrate detection

Flip the last bit: 1011011111. Dividing by 10011 leaves 0001, which is nonzero, so this error is detected. A zero syndrome would mean no detected error, not proof of no corruption.

**Final answer:** CRC=1110; transmitted frame=1011011110; uncorrupted receiver remainder=0000.

#### What this result means

Some software CRCs use different initial/reflection/final conventions; this answer follows the polynomial-division question’s stated textbook model.