Question

What is the purpose of using modulo 2 arithmetic rather than binary arithmetic in computing an fcs?

Answer 1

The purpose of using modulo 2 arithmetic in computing an FCS is to detect transmission errors through simple and efficient calculations. It provides a checksum that can be used to verify data integrity, detecting common errors like single-bit and burst errors. This method does not require handling carry operations, simplifying implementation.

Step-by-step explanation:

The purpose of using modulo 2 arithmetic in computing a Frame Check Sequence (FCS) is to provide error detection capability when data packets are transmitted over a network. Modulo 2 arithmetic is a simple, efficient method of calculating a type of checksum that can be used to verify the integrity of the transmitted data. By performing bitwise exclusive OR (XOR) operations on the data bits, modulo 2 arithmetic generates a value that can be appended to the data. When the data is received, the same operations are performed, including the FCS. If the result is zero, it is assumed that the data has not been corrupted during transmission.Modulo 2 arithmetic is used because it resembles binary addition without carry. It simplifies the hardware or software implementation since handling carry operations is not required. Also, modulo 2 arithmetic can detect common errors such as single-bit errors and burst errors that can occur in communication channels, providing a simple yet robust way to ensure data integrity. This method is commonly used in network protocols, for example, in the Cyclic Redundancy Check (CRC).

Answer 2

When using modulo 2 arithmetic it is easy to implement and get the result. Any arithmetic process would work provided it applied the same way in the forward and reverse the process. Modulo 2 arithmetic is performed digit by digit on binary numbers. Each digit is considered independently from its neighbors, numbers are not carried or borrows.