Binary to Decimal Converter

Convert binary numbers to decimal instantly. Transform base-2 numbers into standard base-10 decimal notation for calculations and analysis.

How to Use

  1. Enter your binary number
  2. Decimal value appears instantly
  3. View optional step-by-step breakdown
  4. Copy the decimal result

Features

  • Instant binary to decimal conversion
  • Handles large binary numbers
  • Shows conversion steps
  • Real-time calculation
  • Signed/unsigned options
  • No length limitations

About This Tool


Binary to decimal conversion translates base-2 numbers (using only 0 and 1) into our familiar base-10 decimal system. This is essential for understanding what binary values actually represent.

The conversion uses positional notation: each binary digit position represents a power of 2, starting from 2^0 on the right. Multiply each bit by its position value and sum the results.

For example, binary "1101" = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13 in decimal. Each 1 contributes its position's power of 2 to the total.

Our converter handles both small and large binary numbers efficiently. It can also show the step-by-step calculation, helping you understand and verify the conversion process.

This is a fundamental skill in computer science and programming, where understanding binary representation is essential for working with data types, memory, and low-level operations.

Frequently Asked Questions

How does binary to decimal work?
Each binary position represents a power of 2 (1, 2, 4, 8, 16...). Sum the powers where there's a 1 to get the decimal value.
What's the largest binary I can convert?
The tool handles very large binary numbers. Practical limits depend on browser memory for extremely long inputs.
What about negative binary numbers?
The converter can handle two's complement signed numbers if specified. Otherwise, it treats input as unsigned.
Why is binary base-2?
Computers use binary because electronic circuits have two states: on (1) and off (0), making base-2 natural for digital systems.
Can I see the calculation steps?
Yes, the tool can show how each bit position contributes to the final decimal value.

Convert binary numbers to decimal instantly. Transform base-2 numbers into standard base-10 decimal notation for calculations and analysis.

Key Features

  • Instant binary to decimal conversion
  • Handles large binary numbers
  • Shows conversion steps
  • Real-time calculation
  • Signed/unsigned options
  • No length limitations

How to Use This Tool

  1. Enter your binary number
  2. Decimal value appears instantly
  3. View optional step-by-step breakdown
  4. Copy the decimal result
Binary to decimal conversion translates base-2 numbers (using only 0 and 1) into our familiar base-10 decimal system. This is essential for understanding what binary values actually represent. The conversion uses positional notation: each binary digit position represents a power of 2, starting from 2^0 on the right. Multiply each bit by its position value and sum the results. For example, binary "1101" = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13 in decimal. Each 1 contributes its position's power of 2 to the total. Our converter handles both small and large binary numbers efficiently. It can also show the step-by-step calculation, helping you understand and verify the conversion process. This is a fundamental skill in computer science and programming, where understanding binary representation is essential for working with data types, memory, and low-level operations.

Benefits

  • Understand binary values
  • Verify binary calculations
  • Convert for programming
  • Educational learning tool

Frequently Asked Questions

How does binary to decimal work?

Each binary position represents a power of 2 (1, 2, 4, 8, 16...). Sum the powers where there's a 1 to get the decimal value.

What's the largest binary I can convert?

The tool handles very large binary numbers. Practical limits depend on browser memory for extremely long inputs.

What about negative binary numbers?

The converter can handle two's complement signed numbers if specified. Otherwise, it treats input as unsigned.

Why is binary base-2?

Computers use binary because electronic circuits have two states: on (1) and off (0), making base-2 natural for digital systems.

Can I see the calculation steps?

Yes, the tool can show how each bit position contributes to the final decimal value.

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