Binary to Decimal Converter

Convert binary numbers to decimal instantly with step-by-step explanations.

From Base

Binary (Base 2)

To Base

Decimal (Base 10)

Enter Binary Number

Result:

...

How it's done:

Common Binary to Decimal Examples

1010₂ = 10₁₀

1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10

11001₂ = 25₁₀

1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 16 + 8 + 0 + 0 + 1 = 25

100101₂ = 37₁₀

1×2⁵ + 0×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32 + 0 + 0 + 4 + 0 + 1 = 37

111111₂ = 63₁₀

1×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 1×2⁰ = 32 + 16 + 8 + 4 + 2 + 1 = 63

Frequently Asked Questions

What is a binary number?

A binary number is a number expressed in the base-2 numeral system, which uses only two digits: 0 and 1. Each position represents a power of 2, starting from the rightmost position (2⁰).

How do I convert binary to decimal?

To convert binary to decimal, multiply each digit by its corresponding power of 2 and sum the results. Start from the rightmost digit (2⁰) and work your way left.

Why is binary used in computers?

Binary is used in computers because electronic circuits can easily represent two states (on/off, high/low voltage) which correspond to 1 and 0. This makes binary the most practical number system for digital electronics.