Gray code, also called reflected binary code, is an ordering of binary numbers where any two consecutive values differ in only one bit. It is used in rotary encoders, Karnaugh maps and error-resistant signalling.

How do you convert binary to Gray code?

The Gray code of a number n is `n XOR (n >> 1)`. The most significant bit stays the same and each lower Gray bit is the XOR of two adjacent binary bits.

How do you convert Gray code back to binary?

You XOR each Gray bit with all the more-significant bits already decoded. Iteratively, `binary = gray; while (gray >>= 1) binary ^= gray;` reconstructs the original integer.

Why does only one bit change between consecutive values?

Because the XOR-with-shift construction guarantees that incrementing by one flips exactly one bit. This minimises errors in mechanical position encoders, where multiple simultaneous bit changes could be misread.

Is there a maximum value?

This tool uses JavaScript's 32-bit bitwise operators, so it handles unsigned integers up to 2,147,483,647 reliably. Larger values may overflow the 32-bit XOR and shift operations.

Gray Code Converter — Gera Tools

What this tool does

This converter translates between ordinary integers and Gray code (binary-reflected code). In Gray code, every step from one number to the next flips exactly one bit, which is why it is the standard encoding for rotary and linear position sensors, and why it makes Karnaugh-map adjacency work.

How it works

Encoding an integer n to Gray code is a one-liner:

gray = n ^ (n >> 1)

The top bit of the Gray code equals the top bit of the binary, and each lower Gray bit is the XOR of two neighbouring binary bits. That XOR is exactly what cancels out all but one bit-change between consecutive numbers.

Decoding a Gray value back to a plain integer accumulates XORs from the most-significant bit downward:

binary = gray;
while (gray >>= 1) {
  binary ^= gray;
}

Each binary bit is the running XOR of every Gray bit at or above its position.

Example

The integer 5 is 101 in binary. Its Gray code is 101 ^ 010 = 111. The integer 6 is 110, whose Gray code is 110 ^ 011 = 101 — differing from the Gray code of 5 in just one bit, which is the defining property.

Notes

The tool pads both the binary and Gray strings to the same width so the single-bit difference is easy to spot.
Decoding ignores anything that is not 0 or 1; encoding requires a non-negative decimal integer.