A data packet uses CRC with a generator polynomial of x^3 + x + 1. If the data bits are 1011, which CRC remainder bits should be appended to detect errors?

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Computer Networks - Physical and Data Link Layer

A data packet uses CRC with a generator polynomial of x^3 + x + 1. If the data bits are 1011, which CRC remainder bits should be appended to detect errors?

A'000' after dividing data by polynomial

B'000' because CRC always appends zeros

C'111' after adding parity bit

D'100' after dividing data by polynomial

Step-by-Step Solution

Solution:

Step 1: Understand CRC calculation
CRC divides data appended with zeros by the generator polynomial and uses the remainder as CRC bits.
Step 2: Perform division for data 1011 and polynomial x^3+x+1
Dividing 1011 (with 3 zeros appended) by polynomial gives remainder 100.
Final Answer:
'100' after dividing data by polynomial -> Option D
Quick Check:
CRC remainder = '100' [OK]

Quick Trick: CRC remainder from polynomial division is appended [OK]

Common Mistakes:

MISTAKES

Confusing CRC remainder with parity bits
Assuming CRC always appends zeros
Skipping polynomial division step

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More Computer Networks Quizzes

A data packet uses CRC with a generator polynomial of x^3 + x + 1. If the data bits are 1011, which CRC remainder bits should be appended to detect errors?

Step 1: Understand CRC calculation

Step 2: Perform division for data 1011 and polynomial x^3+x+1

Final Answer:

Quick Check:

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