How this calculator works
Number positions from left to right starting at one. Powers of two are parity positions; other positions carry data. Each even-parity check covers positions having its bit set in the position number. XORing the positions of all received one bits gives the syndrome. With at most one error, it identifies the flipped position. Ordinary Hamming codes do not have the extra overall parity bit used by SECDED.
Formula
n = 2^r - 1; data bits = n - r. Syndrome = XOR of the 1-based indices whose code bits are 1.
Worked example
In the stated left-to-right convention, payload 1011 encodes to 0110011 in Hamming(7,4). Changing position 5 gives 0110111; its syndrome is 5 and correcting that position restores 1011.
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Frequently asked questions
Why is my codeword different from another tool?
Some tools number from the right or reverse payload order. This page explicitly numbers from the left.
Can it safely correct two errors?
No. Two errors can resemble a different single error. Correction assumes at most one flipped bit.
Does a zero syndrome guarantee a clean word?
No. Some patterns of multiple errors are themselves valid codewords and go undetected.