Question

Given the CRC-3 polynomial x³ + x² + 1 and the hex input data of A767, calculate:

a) CRC checksum
b) Binary equivalent of A767
c) XOR operation result
d) Two's complement of A767

Answer 1

To calculate the CRC checksum using the CRC-3 polynomial x³ + x² + 1, convert the input data to binary and perform a XOR operation with the polynomial.

Step-by-step explanation:

The CRC-3 polynomial x³ + x² + 1 is used to calculate a CRC checksum, which is a type of error-detecting code. To calculate the CRC checksum, follow these steps:

1. Convert the hex input data A767 to binary. A767 is equal to 1010011101100111 in binary.
2. Append three zeroes to the binary data to account for the three terms in the CRC-3 polynomial.
3. Perform a XOR operation on the binary data with the CRC-3 polynomial. This involves dividing the binary data by the CRC-3 polynomial and taking the remainder.
4. The resulting binary checksum is the CRC checksum of the input data. In this case, the CRC checksum is 111.

The binary equivalent of A767 is 1010011101100111. The XOR operation result is 111, which is the CRC checksum. The two's complement of A767 is the binary equivalent of A767 with all bits flipped and then adding 1. In this case, the two's complement of A767 is -2457 in decimal.