Decimal to Gray Code Converter [2025]

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Convert decimal numbers to Gray code format. Perfect for digital circuit design and encoding applications.

✓ Real-time Conversion✓ Adjustable Bit Length✓ Zero Padding

Key Features

  • Convert decimal numbers to both binary and Gray code representations.
  • Choose between 4, 8, 16, or 32-bit output formats.
  • Optional zero padding for consistent output length.
  • Real-time validation and error checking.
  • One-click copy functionality for both binary and Gray code outputs.
  • Support for non-negative integers within bit-length range.
  • Clear, readable output format.
  • Instant conversion with no page reloads.

Common Use Cases

Digital Design

  • • Rotary encoders
  • • Digital circuits
  • • Signal processing
  • • Error detection

Computer Science

  • • Algorithm design
  • • Data encoding
  • • Binary operations
  • • Code optimization

Applications

  • • Position sensors
  • • Data conversion
  • • Digital displays
  • • Error correction

Frequently Asked Questions

What is Gray code?

Gray code, also known as reflected binary code, is a sequence of binary numerals where adjacent numbers differ by only one bit. This property makes it particularly useful in error detection and digital encoding applications, as it minimizes the risk of errors when transitioning between values.

Why use Gray code?

Gray code is particularly useful in applications where binary values change sequentially, as it eliminates the possibility of spurious outputs during transitions. This makes it ideal for rotary encoders, digital displays, and error detection systems where multiple bit changes could lead to incorrect readings.

How do I choose the right bit length?

The bit length you choose should be based on the range of numbers you need to represent. For example, 8 bits can represent numbers from 0 to 255, while 16 bits can handle values up to 65,535. Choose the smallest bit length that can accommodate your maximum value while considering any system requirements for consistent data width.

What's the purpose of zero padding?

Zero padding ensures that all output values have the same number of bits, which is often required in digital systems and data protocols. For example, with 8-bit zero padding, the number 5 (binary 101) would be represented as 00000101, making it easier to process and maintain consistent data width in your applications.

Technical Details

How the Conversion Works

The conversion process follows these steps:

  1. The decimal number is first converted to its binary representation
  2. The most significant bit (leftmost) of the Gray code is the same as the binary
  3. Each subsequent bit is calculated by XORing adjacent bits of the binary number
  4. The result is formatted according to the selected bit length and padding options

For example, converting decimal 5:

  • Decimal: 5
  • Binary: 0101
  • Gray Code: 0111

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