In cyclic redundancy checking, how does the size of the generator polynomial (divisor) compare to the size of the CRC value that is appended?

Introduction / Context:
CRC design uses a generator polynomial of degree r. The division process yields a remainder of r bits, which is appended to the frame as the CRC field. Knowing the exact relationship between the generator degree and the remainder length is essential for implementing and verifying CRC algorithms correctly.

Given Data / Assumptions:

• Let the generator polynomial have degree r.
• The appended CRC (remainder) contains r bits.
• Polynomial representation uses binary coefficients over modulo-2 arithmetic.

Concept / Approach:
A polynomial of degree r has r+1 coefficients (from x^r down to x^0). Therefore, the generator (divisor) has r+1 bits, while the CRC remainder has r bits. This creates the precise one-bit difference asked in the question: the divisor is one bit longer than the CRC value appended to the frame.

Step-by-Step Solution:

Verification / Alternative check:
Examples: CRC-16 uses a 17-bit generator and a 16-bit remainder; CRC-32 uses a 33-bit generator and a 32-bit remainder. These well-known cases confirm the general rule and the answer.

Why Other Options Are Wrong:

• The same size: contradicted by all standard CRCs.
• One bit less / Two bits more: do not match the polynomial degree relationship.
• None: incorrect since a specific relationship exists.

Common Pitfalls:
Confusing polynomial degree (r) with bit length; forgetting that the highest-order coefficient implies one additional bit in the generator beyond the remainder length.

Final Answer:
One bit more than