Reflected binary Gray code is an alternative binary numeral system where two successive values differ by only a single bit. In physical rotary shaft encoders, optical linear encoders, and digital communications, natural binary transitions often change multiple bits simultaneously (for example, transitioning from 0111 to 1000 flips all four bits), which introduces transient glitch states if individual bit switches settle unevenly. Gray code eliminates these race conditions by ensuring single-bit transitions.

This engineering utility converts binary values to reflected Gray code using the fundamental XOR identity: Gray = Binary XOR (Binary >> 1). It displays the complete mathematical derivation step-by-step, supports reverse Gray-to-binary decoding, converts decimal numbers to Binary-Coded Decimal (BCD 8421) nibbles, and provides an interactive 4-bit truth table comparing decimal values 0 through 15 across pure binary, Gray code, and BCD.

For example, entering binary 1010 (decimal 10) shifts right by 1 to 0101; bitwise XORing 1010 and 0101 produces reflected Gray code 1111.

All bitwise derivations execute client-side in your web browser with JavaScript. No binary strings or logic operations are uploaded to external servers.