Free Binary to Decimal Converter

Convert binary numbers (base-2) to decimal numbers (base-10) instantly with our free online converter. Perfect for programming students, computer science learners, software developers, and anyone working with binary data. Simply enter your binary number and get the decimal equivalent immediately. No registration required, works offline, and handles any length of binary input with 100% accuracy.

Maximum 64 digits. Only 0 and 1 are allowed.
Enter a binary number above
Click the result to copy to clipboard

Quick Examples

1010
Binary
10
Decimal
11001
Binary
25
Decimal
101010
Binary
42
Decimal
11111111
Binary
255
Decimal

How Binary to Decimal Conversion Works

1

Understanding Binary System

Binary is a base-2 number system using only digits 0 and 1. Each position represents a power of 2, starting from 2⁰ on the right.

Example: 1 0 1 1 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰
2

Calculate Powers of 2

Multiply each binary digit by its corresponding power of 2, then sum all the results.

Calculation: 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11
3

Get Decimal Result

The sum of all calculations gives you the decimal equivalent of the binary number.

Instant Conversion

Convert binary to decimal instantly with real-time validation and error checking.

Input Validation

Smart validation ensures only valid binary numbers (0s and 1s) are processed.

Step-by-Step

See detailed conversion steps to understand how binary to decimal conversion works.

Who Uses This Tool?

Programmers

Convert binary data, debug code, and work with bit operations

Students

Learn number systems, complete assignments, and understand concepts

Engineers

Design digital circuits, work with embedded systems, and analyze data

Educators

Teach number systems, create examples, and demonstrate conversions