// Numbers
Gray Code Converter online
Convert between Gray code and binary, decimal, hex, or octal - runs in your browser
by
CHUNKY
MUNSTER
MUNSTER
Gray Code Converter is a specialized tool for digital engineers and programmers working with reflected binary code. This system, also known as cyclic code, ensures that consecutive values differ by exactly one bit, which is critical in hardware applications like rotary encoders and error correction. This tool provides instant translation between standard binary and Gray code across multiple bases.
In a standard binary counter, multiple bits can flip at once, leading to transient errors in physical systems. Using this gray code calculator helps you design more reliable state machines and position sensors by utilizing single-bit transitions. Frank Gray's innovation minimizes ambiguity during mechanical state changes. Whether you need a binary to gray code translation or a back-conversion to decimal, our tool handles the bit-level XOR logic exactly.
The most significant bit stays the same. Each subsequent bit is XOR'd with the previous binary bit: G[i] = B[i] XOR B[i-1]. Example: binary 1011 → Gray: 1=1, 1 XOR 0=1, 0 XOR 1=1, 1 XOR 1=0 → Gray = 1110.
The MSB stays. Each subsequent binary bit is XOR'd with the previous binary bit (not Gray bit): B[i] = G[i] XOR B[i-1]. The process works left to right.
Frank Gray patented the reflected binary code in 1953 while working at Bell Labs. The "reflected" name comes from the construction method: the sequence is built by taking the n-bit code and appending its mirror image with a leading 1-bit added.
Gray code sequences appear in Hamiltonian paths on hypercube graphs, in puzzles like the Tower of Hanoi (the solution sequence corresponds to Gray code), and in minimising logic expressions using Karnaugh maps.
For related logic tools, check out our Binary to Decimal converter, BCD Converter, and the Bitwise Calculator. Bookmark this page whenever you need a reliable Gray Code Converter.