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Binary to Decimal Converter

Convert between binary and decimal number systems with this free online calculator. See step-by-step calculations and learn about number conversion.

Number Converter

2
10
16

Number Systems Explained

Binary Number System

Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit position represents a power of 2, with the rightmost digit representing 2⁰ (1), the next digit to the left 2¹ (2), then 2² (4), and so on.

Binary Example

1101₂ = 1×2³+1×2²+0×2¹+1×2⁰ = 13₁₀

Decimal Number System

Decimal is the base-10 number system we use everyday. It uses ten digits: 0-9. Each digit position represents a power of 10, with the rightmost digit representing 10⁰ (1), the next digit to the left 10¹ (10), then 10² (100), and so on.

Decimal Example

653₁₀ = 6×10²+5×10¹+3×10⁰

Conversion Table

BinaryDecimalHexadecimal
00000
00111
01022
01133
10044
10155
11066
11177
100088
100199
101010A
101111B
110012C
110113D
111014E
111115F

How to Convert Binary to Decimal

Binary to Decimal Conversion

To convert a binary number to decimal, multiply each digit by its corresponding power of 2 and add the results.

Formula

decimal = d₀×2⁰ + d₁×2¹ + d₂×2² + ...

Example

Binary Number111001
Power of 22⁵2⁴2⁰
111001₂ = 1⋅2⁵+1⋅2⁴+1⋅2³+0⋅2²+0⋅2¹+1⋅2⁰ = 32+16+8+0+0+1 = 57₁₀