Question 1

What is a Hamming code and how does it correct errors?

Accepted Answer

A Hamming code is a linear error-correcting code that places parity bits at positions 1, 2, 4, 8, 16, … (powers of two) of a codeword. Each parity bit covers all positions whose binary address has the corresponding bit set. When a codeword is received, the decoder XORs those covered bits to compute a syndrome: syndrome = 0 means no error, syndrome = p means position p was flipped and can be corrected by flipping it back. Standard Hamming corrects any single-bit error per codeword.

Question 2

What is SECDED and how does it differ from plain Hamming?

Accepted Answer

SECDED (Single-Error Correction, Double-Error Detection) adds one extra overall parity bit covering the entire codeword. With it, the decoder can still correct any single-bit error AND detect (but not correct) any two-bit error. The rule: syndrome = 0 with overall parity OK = no error; syndrome ≠ 0 with overall parity mismatch = correctable single error at the syndrome position; syndrome ≠ 0 with overall parity OK = uncorrectable double-bit error; syndrome = 0 with overall parity mismatch = error in the overall parity bit itself.

Question 3

Which Hamming code variants are supported?

Accepted Answer

Three standard variants: Hamming(7,4) with 4 data bits and 3 parity bits, Hamming(15,11) with 11 data bits and 4 parity bits, and Hamming(31,26) with 26 data bits and 5 parity bits. You can also let the tool auto-pick the smallest variant that fits your data length, or use the arbitrary-length encoder that computes p = ⌈log2(k + p + 1)⌉ for any k.

Question 4

Can I inject an error and watch the decoder correct it?

Accepted Answer

Yes. After encoding, click any bit (parity or data) to flip it and inject a single-bit error — the decoder recomputes the syndrome live, highlights the flipped position, corrects it, and shows the recovered data. For double-bit-error testing with SECDED enabled, flip two positions and the tool flags the uncorrectable double error instead of miscorrecting.

Question 5

What extra features does this tool have versus other Hamming calculators?

Accepted Answer

(1) Three standard variants plus arbitrary-length encoding. (2) Even/odd parity mode toggle. (3) Per-parity-bit coverage display (which positions each parity bit covers and the values it sees). (4) Live syndrome computation with binary display. (5) Interactive single- and multi-bit error injection. (6) SECDED extended Hamming with double-error detection. (7) Step-by-step corrected codeword and recovered data. (8) Copy codeword / recovered data. (9) History (localStorage, last 20). (10) Shareable URL with full state encoded. (11) Color-coded parity vs data bits. (12) Auto-variant picker. 100% client-side — no uploads, no ads.

Hamming Code Error-Correction Calculator

Codeword — click a bit to flip

Decode & syndrome

Parity-bit coverage (3 parity bits)

How to use

Codeword — click a bit to flip

Decode & syndrome

Parity-bit coverage (3 parity bits)