Gray Code to Binary Converter [2025]

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Convert Gray code back to binary with step-by-step process. Essential for decoding rotary encoder outputs and digital signal processing.

✓ Customizable Bit Length✓ Step-by-Step Process✓ Decimal Output

Enter a binary number in Gray code format (e.g., 1111)

Key Features

  • Convert Gray code to standard binary representation with ease.
  • Choose between 4, 8, 16, or 32-bit output formats.
  • Optional zero padding for consistent output length.
  • View detailed step-by-step conversion process.
  • Automatic decimal representation of results.
  • Real-time input validation and error checking.
  • Copy functionality for quick result sharing.
  • Educational conversion step display.

Common Use Cases

Digital Electronics

  • • Rotary encoders
  • • Position sensors
  • • Signal processing
  • • Data acquisition

System Analysis

  • • Debug outputs
  • • Protocol analysis
  • • Error detection
  • • Data validation

Development

  • • Code verification
  • • Testing tools
  • • Documentation
  • • Learning aids

Frequently Asked Questions

How does the conversion work?

The conversion from Gray code to binary follows a specific process where each binary digit is determined by XORing the current Gray code bit with the previous binary result. The first bit remains the same, and subsequent bits are calculated sequentially. Our tool shows this process step-by-step for educational purposes.

When do I need to convert Gray code to binary?

Converting from Gray code to binary is necessary when working with devices like rotary encoders, processing sensor data, or debugging digital systems that use Gray code encoding. It's also useful in educational contexts when learning about digital encoding schemes and binary operations.

What's the significance of bit length?

The bit length setting ensures your conversion matches your system's requirements. For example, 8-bit systems require 8-bit outputs, while 16-bit systems need 16-bit values. Selecting the correct bit length helps maintain compatibility with your target system or protocol.

Why show the decimal equivalent?

The decimal representation provides a more familiar numeric value that can be useful for verification and understanding. When working with position encoders or other devices, the decimal value often represents a meaningful measurement or position that's easier to interpret than binary.

Technical Details

Gray Code to Binary Conversion Process

The conversion algorithm follows these steps:

  1. Keep the first bit of the Gray code as the first binary bit
  2. For each subsequent bit:
    • XOR the current Gray code bit with the previous binary result
    • The result becomes the current binary bit
  3. Convert the resulting binary to decimal if needed

Example conversion of Gray code 1111:

  • Gray: 1111
  • Step 1: First bit = 1
  • Step 2: 1 XOR 1 = 0
  • Step 3: 0 XOR 1 = 1
  • Step 4: 1 XOR 1 = 0
  • Binary: 1010
  • Decimal: 10

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