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Binary ⇄ Gray Code Converter

Quickly convert values between binary and Gray code

Gray to Binary

Result

Result based on the provided information

Binary to Gray

Result

Result based on the provided information

Related Features

Binary ↔ Decimal
Binary ↔ Text
Binary ↔ Hexadecimal
Binary ↔ Octal
Binary ↔ ASCII
Binary ↔ Base64
Binary ↔ Gray Code
Binary ↔ BCD (Binary-Coded Decimal)

Binary to Gray Code and Gray Code to Binary Converter – Online, Fast, and Free

Do you need to convert binary numbers to Gray Code—or Gray Code back to binary—quickly and easily?

Fastools offers a free online Binary to Gray Code and Gray Code to Binary converter, ideal for students, programmers, technicians, and professionals who want to understand how Gray Code works and how it’s applied in digital systems. All directly in your browser—no installation or sign-up required.

Simply enter your binary or Gray Code value, select the desired conversion direction, and click “Convert”. In seconds, you’ll get an accurate result, following the standard Gray Code algorithm— widely used to minimize errors in reading and transmission systems.

Our Binary to Gray Code converter is ideal for digital logic studies, electronics, computer architecture, signal encoding, and systems where minimizing transition errors between states is critical.

How to use the Binary to Gray Code and Gray Code to Binary converter?

  • 1️⃣ Select the desired mode: Binary → Gray Code or Gray Code → Binary.
  • 2️⃣ Enter or paste your value in the input field.
  • 3️⃣ Click “Convert” to get your result instantly.
  • 4️⃣ Copy, share, or use the converted value as needed.

Why use the Fastools Gray Code converter?

  • ✅ 100% free, fast, and online conversion
  • ✅ Accurate conversion following the official Gray Code standard
  • ✅ Ideal for digital logic, electronics, and embedded systems
  • ✅ Simple, intuitive, and easy-to-use interface
  • ✅ Compatible with computers, tablets, and smartphones

Benefits of using our Gray Code conversion tool

  • 📊 Learn how Gray Code works and how it relates to the binary system
  • ⚡ Instantly convert binary values and Gray codes
  • 🎯 Perfect for digital electronics, automation, and computing studies
  • 💻 Use directly in your browser—no apps to install

Can I use this converter to learn Gray Code, binary, or digital systems?

Yes! This tool is excellent for anyone studying number systems, Gray Code, error reduction in digital circuits, rotary encoders, and the fundamentals of electronics and computing.

Start converting Binary to Gray Code and Gray Code to Binary—quickly, accurately, and completely free—with Fastools. Make your digital systems studies and projects much simpler!

What is Binary to Gray Code conversion?

Binary to Gray Code conversion transforms traditional binary numbers into a special encoding where only one bit changes between consecutive values. This feature reduces errors during transitions and readings in digital systems.

Gray Code is widely used in digital electronics, embedded systems, rotary encoders, analog-to-digital converters, and circuits where precision in state transitions is critical.

What is converting Binary to Gray Code used for?

Converting binary to Gray Code helps avoid ambiguities caused by simultaneous changes in multiple bits, improving the reliability of readings in physical and digital systems.

  • Reducing errors in rotary encoders and sensors
  • Applications in digital electronics and industrial automation
  • Safe conversion of binary states
  • Studying computer architecture and logic circuits

How does Binary to Gray Code conversion work?

The conversion keeps the most significant bit (MSB) the same as in the original binary. The remaining bits are obtained by applying the XOR operation between the current bit and the previous bit of the binary number.

Basic rule

Gray[0] = Binário[0]
Gray[n] = Binário[n] XOR Binário[n-1]

Practical example

Binary: 1011
Gray Code: 1110

Notice that between consecutive Gray Code values, only one bit changes, minimizing read errors during transitions.

Important notes

  • Gray Code is not used for direct arithmetic calculations.
  • Its main advantage is stability during transitions.
  • It’s very common in sensors and physical hardware.

What is Gray Code to Binary conversion?

Gray Code to Binary conversion is the reverse process, where the Gray sequence is transformed back into a standard binary number, enabling standard digital calculations and processing.

What is converting Gray Code to Binary used for?

This conversion is necessary when data from sensors, encoders, or circuits in Gray Code must be interpreted by computer systems, microcontrollers, or software.

  • Reading rotary encoders
  • Digital signal processing
  • Converting logic states for computation
  • Hardware-software integration

How does Gray Code to Binary conversion work?

The most significant bit of the binary remains the same as in the Gray Code. Subsequent bits are obtained by applying the XOR operation between the previous binary bit and the current Gray bit.

Basic rule

Binary[0] = Gray[0]
Binary[n] = Binário[n-1] XOR Gray[n]

Practical example

Gray Code: 1110
Binary: 1011

By cumulatively applying the XOR operation, the original binary number is fully reconstructed.

Possible conversion errors

  • Incorrect application of the XOR operation.
  • Error in identifying the most significant bit (MSB).
  • Incorrect reading of the Gray code signal in physical sensors.

Did you know?

  • Gray Code was developed by Frank Gray in 1947.
  • It is also known as reflected binary code.
  • It is widely used in robotics and automation.