Question

Consider all the possibile strings of two data bits (K = 2). A CRC is attached at the end of each string during transmission to create the corresponding codework. The CRC is computed using the generator polynomial g(D) = D⁴ + D³ + D² + 1.

Generate all 4 possible codewords

Answer 1

The student's question involves calculating the CRC codewords for four possible two-bit strings using the generator polynomial g(D) = D⁴ + D³ + D² + 1. Codewords are created by appending four zeros to each data string, dividing by the polynomial, and attaching the remainder to the original data bits.

Step-by-step explanation:

The question is about generating codewords for two data bits using a given generator polynomial for the CRC (Cyclic Redundancy Check) coding process. The generator polynomial in question is g(D) = D⁴ + D³ + D² + 1. Because the data is 2 bits long, there are four possible strings: 00, 01, 10, and 11. To generate the codeword, each data string is multiplied by the polynomial, which essentially appends four zero bits (representing the polynomial's degree) to the data string and then dividing it by the generator polynomial to find the remainder which is the CRC. The CRC is then attached to the original data bits to create the codeword. Using polynomial long division, we find the CRC for each of the four data strings and attach it to create the four codewords.