In Cyclic Redundancy Check (CRC) error detection, there is considered to be no error at the receiver if the computed remainder at the receiver is equal to which value?

Introduction / Context:
CRC (Cyclic Redundancy Check) is a widely used error-detecting code in data communications and storage. A frame or block is divided by a generator polynomial, and the remainder is appended at the sender. At the receiver, the same division is performed. Understanding what the receiver expects as the result of this division is fundamental to interpreting CRC checks correctly.

Given Data / Assumptions:

• Sender computes a CRC remainder using an agreed generator polynomial.
• The sender appends this CRC remainder to the data before transmission.
• The receiver divides the entire received bitstream (data + CRC) by the same generator polynomial.

Concept / Approach:
The CRC property guarantees that if no bit errors have occurred and both ends use the same generator, the received codeword (data with CRC) is exactly divisible by the generator polynomial. In arithmetic terms, a correct frame yields a zero remainder at the receiver. A nonzero remainder indicates corruption or mismatch.

Step-by-Step Solution:

Verification / Alternative check:
Test with a simple generator (for example, G = 1101) on a small data sequence. Verify that the appended CRC makes the full sequence divisible by G with zero remainder; flipping any bit typically yields a nonzero remainder.

Why Other Options Are Wrong:

• Equal to the remainder at the sender: The receiver does not recompute and compare remainders directly; it divides the whole codeword and expects a zero remainder.
• Nonzero: A nonzero remainder signals error.
• The quotient at the sender: The quotient is irrelevant to the check outcome.

Common Pitfalls:
Confusing parity-like comparison with CRC's divisibility test, or assuming the receiver recomputes a remainder on raw data and compares it bitwise rather than checking for a zero remainder on the full codeword.

Final Answer:
zero