How to Use Hamming Code Calculator
Choose encode or decode, then enter a binary string. In encode mode, enter data bits such as 1011 and the calculator inserts parity bits at power-of-two positions. In decode mode, enter a Hamming code word; the tool calculates the syndrome, flips the indicated bit when a single-bit error is detected, and extracts the corrected data bits.
Formula & Theory - Hamming Code Calculator
Hamming code places parity bits at positions 1, 2, 4, 8, and so on. Each parity bit checks positions whose binary index includes that parity bit. This implementation uses even parity by XORing the covered bits. During decoding, the parity failures combine into a syndrome number; a nonzero syndrome points to the bit position to correct.
choose r where 2^r >= dataLength + r + 1
parity[p] = XOR(bits where position & p)
syndrome = sum(failed parity positions)Use Cases for Hamming Code Calculator
Use it to learn error-correcting codes, check homework examples, demonstrate single-bit error correction, build simple digital-logic lessons, or inspect how parity positions and syndromes work in binary data.