The message 1001 is to be transmitted using the CRC polynomial x³ + x + 1 to…
2024
The message 1001 is to be transmitted using the CRC polynomial x³ + x + 1 to protect it from errors. The message that should be transmitted is –
- A.
1001000
- B.
1001100
- C.
1001110
- D.
1001011
- E.
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Correct answer: C
This is a Cyclic Redundancy Check (CRC) problem.
Given:
Message = 1001
Generator polynomial = x3+x+1
→ Binary divisor = 1011
Step 1: Append zeros
Since generator degree = 3, append 3 zeros:
Message = 1001 → 1001000
Step 2: Binary division (mod-2)
Divide 1001000 ÷ 1011
Remainder obtained = 110
Step 3: Final transmitted message
Append remainder to original message:
1001 + 110 = 1001110