Decimal to Gray Code Converter

Convert decimal to Gray code using binary reflected logic

Input
Gray Code Result
0100
Decimal: 7
Binary: 0111

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What is Gray Code?

Gray code, also known as reflected binary code, is a binary numeral system where two successive values differ in only one bit. This property prevents errors in digital communication, rotary encoders, and Karnaugh maps. The conversion uses XOR operation: G = B ^ (B >> 1).

Frequently Asked Questions

Why use Gray code instead of binary?
In binary, multiple bits can change at once (3→4: 011→100, all bits flip). This can cause errors in mechanical switches and asynchronous systems. Gray code changes one bit at a time, eliminating ambiguity.
Where is Gray code used?
Rotary encoders, shaft position sensors, error correction in digital communication, Karnaugh maps, and genetic algorithms. Anywhere signal stability during transitions matters.
How do I convert back from Gray to decimal?
Use our Gray to Decimal converter! The reverse process requires iterative XOR: start with MSB, each next bit is XOR of current Gray bit and previous result.