Gray Code Converter (Decimal ⇄ Binary ⇄ Gray Code)

What Gray code is

Gray code, also called reflected binary code, is an ordering of binary numbers in which any two successive values differ in exactly one bit. That single-bit-change property makes it valuable for rotary encoders, position sensors and state machines, where a glitchy multi-bit transition in ordinary binary could momentarily read a completely wrong value. Converting binary to Gray code is a simple bitwise operation: the first bit stays the same, and every other Gray bit is the XOR of the current binary bit with the one before it, which is the same as computing b XOR (b shifted right by one).

Using this converter

Type a decimal number, a binary string, or a Gray code and the other two boxes update live — so you can go decimal → Gray directly (the way encoder positions and textbook exercises are framed) or decode a Gray value straight back to a plain number. Each field updates the others as you type. Binary to Gray applies g[i] = b[i-1] XOR b[i] per position, and Gray to binary reverses it with a cumulative XOR, so b[i] = b[i-1] XOR g[i]. Only the digits 0 and 1 are accepted, and any other character shows a clear message. Leading zeros are preserved, so an 8-bit pattern stays 8 bits wide.