Gray Code Converter

The "reflected binary code" was first described by the French engineer Émile Baudot (of baud-rate fame) in 1878 for use in telegraphy. Frank Gray, a physicist at Bell Labs, patented the code in 1947 for use in pulse-code modulation — the same era that produced Hamming\'s error-correcting codes and Shannon\'s information theory. Bell Labs patents granted Gray\'s name lasting association with the code despite its earlier provenance.

The single-bit-change property has been critical for rotary and linear position encoders since the 1960s. A sensor reading a binary-coded disk could catch the disk mid-transition and see a garbage value; a Gray-coded disk guarantees that any reading is either correct or off by one position, never wildly wrong. This is why every modern industrial rotary encoder uses Gray code internally, converting to binary on the output side via simple XOR logic.

Modern applications extend beyond encoders. Karnaugh maps use Gray-code axis ordering so adjacent cells differ by one variable, simplifying logic minimization. Flash memory management uses Gray-coded multi-level cells to minimize bit error rates during read-disturb events. And multi-bit counters crossing asynchronous clock domains use Gray-coded bus encoding so synchronizer flip-flops only ever see one changing bit per cycle — dramatically reducing metastability risk.

Enter either a decimal value or a Gray binary code, pick a bit width (3, 4, 6, or 8), and the tool converts in both directions. The sequential table shows every value for that width with only one bit changing from each row to the next — a visual demonstration of the defining Gray-code property.

Conversion formulas: Binary → Gray: G = B XOR (B >> 1) — one shift and one XOR. Gray → Binary: each binary bit is the XOR of all Gray bits from the MSB down to that position. Both are trivial in hardware and in most programming languages. Everything runs client-side; no values leave your browser.