How does Cyclic Redundancy Check (CRC) work for error detection?

CRC treats data as polynomial and divides by generator polynomial, appending remainder as check bits. At receiver, division of received data (including CRC) by same generator should yield zero remainder if no errors. CRC detects all single-bit errors, all burst errors shorter than CRC length, most longer bursts, and all odd-number bit errors (with factor x+1 in generator). Common CRCs: CRC-16, CRC-32 (Ethernet, ZIP). Implementation uses shift registers with XOR feedback matching generator polynomial. CRC is not suitable for correction, only detection.