How to use it
Choose Hamming(7,4) for four data bits or Hamming(15,11) for eleven. Encode inserts parity bits; Check evaluates a received 7- or 15-bit codeword and shows the corrected word under the single-error assumption.
Position and parity convention
The displayed string is numbered left to right starting at position 1. Powers of two are parity positions. Each even-parity check covers positions whose binary position number contains that parity bit.
Worked example
For data 1011 in (7,4) mode, the result is 0110011 with this page’s left-to-right convention. Flipping position 5 gives syndrome 5, so a single-bit correction restores the original codeword and data.
Limits and FAQ
Leading zeroes are preserved. A zero syndrome means all checks passed, not that arbitrary corruption is impossible. Two or more changed bits can produce a misleading syndrome; SECDED and simulation are outside this tool.
How to read the syndrome
Each failed parity check contributes its parity position number. Adding those positions gives the syndrome. Syndrome 0 means no single-bit error was found; a nonzero value identifies the bit to flip only under the one-error assumption.
When Hamming code is useful
Hamming code is useful for learning parity placement and for systems designed around single-error correction. It is not encryption, compression, a checksum for arbitrary files, or protection against bursts of corruption. Real systems may add an overall parity bit (SECDED) or stronger error-correcting codes.