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Base Converter

Convert numbers between binary, decimal, octal, and hexadecimal instantly. Get step-by-step conversions and learn number systems.

Select Number Base

Binary Base 2 (0-1)
Decimal Base 10 (0-9)
Octal Base 8 (0-7)
Hexadecimal Base 16 (0-9, A-F)

Enter Number

Binary → All Bases
Binary (Base 2)

Conversion Results

1010₂ All Bases
Binary (Base 2)
1010
Decimal (Base 10)
10
Octal (Base 8)
12
Hexadecimal (Base 16)
A

Conversion Steps

Number Systems Explained

Binary System (Base 2)

Base
2
Digits
0, 1
Usage
Computers, Digital
Example
1010₂ = 10₁₀

Binary is the fundamental language of computers. Each digit is called a bit (binary digit). 8 bits make a byte. Used in all digital systems and computer programming.

Decimal System (Base 10)

Base
10
Digits
0-9
Usage
Daily life, Math
Example
123₁₀ = 123

The decimal system is the standard system for denoting integer and non-integer numbers. It's the most common system used by humans in daily life and commerce.

Octal System (Base 8)

Base
8
Digits
0-7
Usage
Unix permissions
Example
12₈ = 10₁₀

Octal was used in early computing systems. Today, it's primarily used in Unix file permission systems. Each octal digit represents three binary digits.

Hexadecimal (Base 16)

Base
16
Digits
0-9, A-F
Usage
Programming, Memory
Example
A₁₆ = 10₁₀

Hexadecimal is widely used in computer science and programming. Each hex digit represents four binary digits (a nibble). Commonly used for memory addresses and color codes.

Common Conversions Reference

Decimal Binary Octal Hexadecimal

Why Use Our Base Converter?

Instant Conversion

Convert between binary, decimal, octal, and hexadecimal instantly with accurate results.

Multi-Base Support

Convert between all major number systems: binary, decimal, octal, and hexadecimal.

Step-by-Step Solutions

See detailed conversion steps to understand how the result was obtained.

Visual Representation

Visualize conversions with clear mathematical notation and color-coded results.

Educational Tool

Perfect for students, programmers, and anyone learning about number systems.

Mobile Friendly

Works perfectly on all devices including smartphones, tablets, and desktop computers.