Gray Code to Decimal Converter

Convert Gray code to decimal using inverse XOR logic

Gray Code Input
Decimal Result
7
Gray: 0100
Binary: 0111

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How to Convert Gray Code to Decimal

Converting Gray code back to binary (and decimal) requires iterative XOR: the most significant bit stays the same, then each subsequent bit is XOR of the current Gray bit and the previous binary result. This reverse process recovers the original binary value.

Frequently Asked Questions

How do I manually convert Gray to binary?
Keep first bit as is. For each next bit, XOR the Gray code bit with the previous binary result. Example: Gray 0100 → binary: 0, then 0⊕1=1, 1⊕0=1, 1⊕0=1 → 0111 (decimal 7).
Why would I need this conversion?
Industrial sensors, rotary encoders, and position transducers often output Gray code directly. Converting to decimal gives you actual position values for your application.
What if my Gray code has spaces?
Our converter strips spaces automatically. You can enter formats like "0100", "0 1 0 0", or "01-00" and it will work correctly.