How does Hamming code work for single-error correction?

Hamming code adds parity bits at power-of-2 positions (1, 2, 4, 8...) to enable single-error correction. Each parity bit covers specific data bits: P1 covers positions with LSB=1 in binary, P2 covers positions with bit 1=1, etc. For (7,4) Hamming: 4 data bits + 3 parity bits. On reception, syndrome is computed by recalculating parities; non-zero syndrome indicates error position in binary. SEC-DED (single-error-correct, double-error-detect) adds overall parity bit. Implementation uses XOR trees for parity calculation. Hamming distance of 3 (or 4 for SEC-DED) enables correction capability.