Free Binary to Decimal Converter

Binary to Decimal Converter

Free & Instant - Convert binary numbers (base 2) to decimal numbers (base 10) with perfect accuracy for programming and mathematics

Binary to Decimal Converter

Only 0s and 1s allowed

Binary (Base 2)
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Binary Number System

Binary uses only digits 0 and 1, representing the fundamental language of computers and digital systems. Each position represents a power of 2.

Decimal (Base 10)
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Decimal Number System

Decimal uses digits 0-9 and is the standard number system for everyday mathematics, business calculations, and human-readable numbers.

Why Convert Binary to Decimal?

Programming & Development

Essential for understanding computer operations, debugging bit manipulation code, and working with low-level programming languages.

Computer Science Education

Fundamental concept for students learning about number systems, digital logic, computer architecture, and data representation.

Digital Electronics

Critical for engineers working with microcontrollers, FPGA programming, and understanding digital circuit outputs and configurations.

Network Administration

Important for subnet mask calculations, IP address conversions, and understanding network configurations in binary format.

How It Works

1. Enter Binary

Input your binary number using only 0s and 1s in the converter field.

2. Convert Instantly

Our system calculates the decimal equivalent using base-2 positional notation.

3. Get Result

Copy your decimal result instantly for use in calculations or programming.

Frequently Asked Questions

How do I convert binary to decimal manually?

To convert binary to decimal, multiply each digit by its corresponding power of 2 and sum the results. For example, binary 1011 = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 decimal.

What is the largest binary number I can convert?

Our converter can handle binary numbers up to 32 bits (32 digits), which converts to decimal numbers up to 4,294,967,295. This covers most practical computing applications.

Why do computers use binary instead of decimal?

Computers use binary because digital circuits can easily represent two states (on/off, high/low voltage). This makes binary the most efficient and reliable number system for electronic devices.

Can I convert negative binary numbers to decimal?

This tool converts unsigned binary numbers. For signed binary numbers (using two's complement), you would need a specialized signed binary converter that handles negative values.

Is binary to decimal conversion accurate for all numbers?

Yes, binary to decimal conversion is always 100% accurate because both are exact number systems. Unlike floating-point conversions, there's no precision loss in integer binary-to-decimal conversion.