Binary to Decimal Converter [2025]

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Convert binary (base-2) numbers to decimal (base-10) with step-by-step explanations. Perfect for computer science students and digital system designers.

✓ Batch Conversion✓ Step-by-Step Process✓ Customizable Format

Enter multiple binary numbers separated by spaces, commas, or new lines

Key Features

  • Convert multiple binary numbers simultaneously with batch processing.
  • Adjustable bit length support (8, 16, 32, or 64 bits).
  • Optional zero padding for consistent output format.
  • Detailed step-by-step conversion breakdown.
  • Copy functionality for individual and batch results.
  • Real-time input validation and error checking.
  • Support for multiple input formats (space, comma, or newline separated).
  • Clear error messages for troubleshooting.

Common Use Cases

Education

  • • Number systems
  • • Computer science
  • • Digital logic
  • • Programming basics

Development

  • • Debug binary data
  • • Verify calculations
  • • Protocol analysis
  • • Data conversion

Digital Systems

  • • Hardware design
  • • Memory analysis
  • • Register values
  • • Signal processing

Frequently Asked Questions

How does binary to decimal conversion work?

Binary to decimal conversion works by multiplying each binary digit by its corresponding power of 2 based on its position, then summing these values. For example, the binary number 1101 converts to (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8 + 4 + 0 + 1 = 13 in decimal.

Why use different bit lengths?

Different bit lengths accommodate different numeric ranges and system requirements. 8-bit values range from 0 to 255, 16-bit from 0 to 65,535, and so on. Choosing the appropriate bit length ensures compatibility with your target system or application.

What is zero padding used for?

Zero padding adds leading zeros to make all binary numbers the same length. This is useful for maintaining consistent data width, making outputs more readable, and ensuring compatibility with systems that expect fixed-width binary values.

Can I convert multiple numbers at once?

Yes, you can convert multiple binary numbers simultaneously by separating them with spaces, commas, or newlines. This batch conversion feature is particularly useful when working with multiple values, such as analyzing data dumps or processing multiple register values.

Technical Details

Understanding Binary Numbers

Binary numbers use a base-2 system where each digit represents a power of 2:

  1. Each position represents a power of 2 (2⁰, 2¹, 2², 2³, etc.)
  2. Only digits 0 and 1 are used
  3. The value is calculated by:
    • Multiplying each 1 by its position's power of 2
    • Adding all these values together

Example: Binary 1101

  • 1 in 2³ position = 8
  • 1 in 2² position = 4
  • 0 in 2¹ position = 0
  • 1 in 2⁰ position = 1
  • Total: 8 + 4 + 0 + 1 = 13

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