Question

A message consisting of 64 bits is transmitted over a communication channel using CRC-8 with the polynomial x⁸ + x⁷ + x² + 1. The receiver detects errors in bits 11, 22, 33, and 44. Determine the remainder obtained by the receiver when performing the CRC check. Show the mathematical process with explanation.

Answer 1

The remainder obtained by the receiver in the CRC check is the bits representing the errors: 11, 22, 33, and 44.

Step-by-step explanation:

The CRC-8 polynomial x⁸ + x⁷ + x² + 1 can be represented by 9 bits (8 bits for the polynomial coefficients and 1 bit for the constant term). The message consisting of 64 bits is divided by this 9-bit polynomial using the polynomial division process. The remainder obtained by the receiver in this CRC check will be the bits that represent the errors detected.

In this case, the remainder obtained by the receiver will be the bits 11, 22, 33, and 44, which represent the errors. The remaining bits will be the correct bits of the message.