In cyclic redundancy check (CRC) encoding at the sender, what happens to the quotient obtained during the modulo-2 division by the generator polynomial?

Introduction:CRC (cyclic redundancy check) is a robust error-detection method used in networking and storage. Understanding each artifact of the division process—dividend, divisor (generator), quotient, and remainder—clarifies how transmitters and receivers implement CRC efficiently.

Given Data / Assumptions:

• The sender divides an augmented data polynomial by a generator polynomial using modulo-2 arithmetic.
• The process yields a quotient and a remainder (the CRC).
• The receiver re-checks integrity using the same generator.

Concept / Approach:In CRC, only the remainder is significant for transmission integrity; it is appended to the data as the Frame Check Sequence (FCS). The quotient is an intermediate computational result with no role in verification and is therefore discarded. At the receiver, the concatenated data+CRC is divided by the same generator; a zero remainder indicates no detectable error.

Step-by-Step Solution:1) Sender forms the message polynomial (data shifted by k bits where k = degree of generator).2) Compute modulo-2 division: message / generator → quotient and remainder.3) Append the remainder (CRC) to the original data; ignore the quotient.4) Receiver divides (data + CRC) by the generator and expects remainder = 0.

Verification / Alternative check:Standards such as Ethernet specify a 32-bit CRC appended to frames; no field carries the quotient—confirming it is not transmitted.

Why Other Options Are Wrong:

• becomes the dividend/divisor: incorrect; the receiver’s dividend is the received frame; the divisor remains the agreed generator polynomial.
• is the remainder: wrong; the remainder is the FCS, not the quotient.
• None of the above: invalid because the quotient is discarded.

Common Pitfalls:Confusing intermediate math artifacts with transmitted fields; only the remainder (CRC) is sent, not the quotient.

Final Answer:is discarded