How does the cyclic redundancy checksum work??

Question

What will be an ideal response?

Answer 1

?The CRC error-detection method treats the packet of data to be transmitted (the message) as a large polynomial. The rightmost bit of the data becomes the x0 term, the next data bit to the left is the x1 term, and so on. When a bit in the message is 1, the corresponding polynomial term is included. The transmitter takes this message polynomial and, using polynomial arithmetic, divides it by a given generating polynomial, and produces a quotient and a remainder. The quotient is discarded, but the remainder (in bit form) is appended to the end of the original message polynomial, and this combined unit is transmitted over the medium. When the data plus remainder arrive at the destination, the same generating polynomial is used to detect an error.
The receiver divides the incoming data (the original message polynomial plus the remainder) by the exact same generating polynomial that was used by the transmitter. If no errors were introduced during data transmission, the division should produce a remainder of zero. If an error was introduced during transmission, the arriving original message polynomial plus the remainder will not divide evenly by the generating polynomial and will produce a nonzero remainder, signaling an error condition.