In cyclic redundancy checking (CRC), what does the term “CRC” refer to within the frame check sequence process?

Introduction / Context:
Cyclic Redundancy Check (CRC) is a robust error-detection method used in data link protocols like Ethernet and PPP. It involves treating bit strings as polynomials over a binary field, dividing by a generator polynomial, and appending a check value. Understanding which quantity is called the “CRC” helps clarify how frames are validated at the receiver.

Given Data / Assumptions:

• Binary division by a generator polynomial (the divisor) is performed on the transmitted bits.
• The process yields a quotient and a remainder.
• The check field appended to the frame is commonly named “CRC.”

Concept / Approach:
The sender computes the remainder after polynomial division (using modulo-2 arithmetic) and appends this remainder to the frame. The receiver divides the entire received bitstream by the same generator; a zero remainder indicates no detected errors. Therefore, “CRC” colloquially names the remainder field that is transmitted as the check value, not the divisor, dividend, or quotient.

Step-by-Step Solution:

Verification / Alternative check:
Ethernet’s 32-bit Frame Check Sequence (FCS) is precisely such a remainder calculated using a standard 32-bit generator polynomial. Packet analyzers report a “Bad FCS” when the computed remainder at the receiver side is nonzero.

Why Other Options Are Wrong:

• The divisor: that is the generator polynomial, not the CRC value.
• The quotient: not transmitted or named as the CRC.
• The dividend: refers to the data (with appended zeros) being divided.
• None: incorrect because the remainder is explicitly the CRC check field.

Common Pitfalls:
Mixing up the generator (divisor) with the remainder; assuming the quotient is useful for checking—it is not used; forgetting that CRC is an error-detection mechanism, not error correction.

Final Answer:
The remainder