A checksum that catches almost everything: treat the message as one giant binary number, divide by a fixed polynomial, and send the remainder along. The receiver divides again — a clean line leaves zero, a single flipped bit anywhere leaves something else. Slide to corrupt a bit and watch the remainder light up.
CRC-8 with polynomial x⁸+x²+x+1 (0x07) is a shift-and-XOR division over GF(2). The sender appends the remainder so the whole frame divides evenly; the receiver re-divides and a non-zero remainder means the frame changed. A fail-loud self-check flips every single bit of a message+CRC frame and throws unless the recomputed CRC differs every time — CRC-8 catches ALL single-bit errors (and all bursts up to 8 bits), the property that makes it worth the eight bits.
No checksum is perfect: a rare pattern of errors can land back on a multiple of the polynomial and slip through (the residual error rate is ~1/2⁸ for random corruption). Single-bit and short-burst detection is guaranteed and is what the self-check verifies.