Question

Consider the cyclic redundancy check (CRC) algorithm. Suppose that the 4-bit generator g is 1001 and the data payload d is 10011010. What are the CRC bits r associated with the data payload d?

Answer 1

The CRC bits (r) are obtained by appending zeros to the original data payload and performing polynomial division using the XOR operation with the generator. The remainder from this division gives us the CRC bits that are appended to the original data.

Step-by-step explanation:

The student is asking about the cyclic redundancy check (CRC) bits that would be associated with a given data payload using a specified generator. The generator g is 1001, and the data payload d is 10011010. To calculate the CRC bits, we must first append three zeros to the data payload (since the generator is 4 bits, we need to append a number of zeros equal to the generator length minus 1). Our modified data is now 10011010000. We then perform polynomial division of the modified data by the generator using the XOR operation, disregarding any remainder that is smaller than the degree of the generator polynomial.

Our dividend (modified data) is 10011010000 and our divisor (generator) is 1001. We perform the division:
100110100001001 | 1001101010010010
After we continue this process and XOR all the bits, we get the remainder which will be the CRC bits. The CRC bits, r, will be appended to the original data to form the message that is transmitted.