Question

Info: 1111101 has to be sent on a data link. The sender and receiver share a polynomial: x³ + x²+ 1

a. Generate the syndrome using CRC
b. Show the actual message to be transmitted

Answer 1

To generate the syndrome using CRC for the binary sequence 1111101 with the polynomial x³ + x² + 1, we append three zeros to the original data, divide by the polynomial using binary division, and append the remainder (CRC checksum) to the original data for transmission.

Step-by-step explanation:

The question asks to generate the syndrome using Cyclic Redundancy Check (CRC) for the given binary sequence 1111101 with the shared polynomial x³ + x² + 1. For CRC, we first append the degree of the polynomial number of zero bits to the original data. Hence, for a 3rd-degree polynomial, we append three zeros, resulting in 1111101000.

We then divide this by the polynomial using binary division. The remainder of this division is the CRC checksum, which is appended to the original data to form the actual message to be transmitted. For simplicity, let's represent the polynomial x³ + x² + 1 as 1101 in binary. The CRC checksum is found by dividing the data (1111101000) by the polynomial (1101), and the actual message is the original data followed by this checksum.