Gray Code Converter

Turn binary numbers into Gray code with n xor n>>1.

What it does

Gray code orders binaries so neighbors flip one bit. Encoders use it to avoid glitches where several bits change at once. Position 10 reads 1010 binary but 1111 Gray.

The tool above takes decimal n and returns Gray decimal, Gray binary, and plain binary. The default 10 matches the worked example, so the page opens showing Gray 15. Type a new n to update all three results.

The rule is g = n xor (n>>1). For 10, binary 1010 shifted is 0101, xor is 1111 for 15. Counting Gray 0,1,3,2,6,7,5,4 shows single flips throughout.

Use Gray for rotary encoders, Karnaugh maps, and clock crossing. For error counts between codes use Hamming distance instead.

This page shows the formula, one full hand checked example at 10, a reference table, and practice checks that run through the tool.

How to use

1. Type decimal n from 0 to 1e9.
2. Read Gray decimal as the main result.
3. Read Gray binary for encoder tracks.
4. Read Binary to compare with input.
5. Count flips between neighbors to verify.
6. Split large ranges into chunks.

Formula

n

Decimal input.

>>1

Right shift one bit (halve floored).

xor

Bitwise exclusive or.

32 bit math assumed. Inputs cap at 1e9 to stay exact and fast.

Worked example

Reference table

Limits

• Nonnegative integers to 1e9 here.
• Binary reflected Gray only.
• No Gray to binary direction here.
• Encoder mechanics (detents, alignment) sit outside.

Common mistakes

• XORing decimal digits instead of bits.
• Shifting left instead of right.
• Expecting Gray order to match binary order.
• Using Gray where Hamming distance is needed.
• Running past 32 bit range.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• Wikipedia: Exclusive or
• Wikipedia: Hamming distance

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