Hamming Code Calculator

Hamming code is a family of error-correcting codes introduced by mathematician Richard Hamming. It adds carefully positioned parity bits to a data word so a receiver can identify and repair a single changed bit. The Hamming (7,4) scheme used here transforms four data bits into a seven-bit codeword. It is a compact demonstration of the same error-control principles used in digital communications, computer memory, storage systems, and embedded electronics. Seven code positions are numbered from one through seven. Parity bits occupy positions one, two, and four because those positions are powers of two. The four original data bits occupy positions three, five, six, and seven. Each parity bit checks a different overlapping group of positions. This calculator uses even parity, meaning every checked group should contain an even number of ones after its parity bit is included. For data bits d1, d2, d3, and d4, parity p1 checks d1, d2, and d4. Parity p2 checks d1, d3, and d4. Parity p4 checks d2, d3, and d4. The resulting order is p1, p2, d1, p4, d2, d3, d4. Encoding 1011 therefore produces 0110011. You can verify each parity group by counting its ones. When a seven-bit code arrives, the receiver repeats the three parity checks. Failed checks form a three-bit syndrome whose numeric value identifies the erroneous position. A syndrome of one points to the first bit, a syndrome of five points to the fifth bit, and a syndrome of zero indicates no single-bit error. Flipping the identified bit restores the original valid codeword. The optional received-code field demonstrates this process and displays the corrected sequence. Standard Hamming (7,4) code guarantees correction of one-bit errors, but it cannot reliably distinguish every two-bit error. Extended Hamming code adds an overall parity bit to provide single-error correction and double-error detection. This calculator intentionally focuses on the classic seven-bit version and even parity. Enter only zeros and ones, with no spaces, prefixes, or separators, so bit positions remain unambiguous.