Universal Base Converter
Understand and calculate number system conversions instantly
Interactive Simulator
What is Base Conversion?
Base conversion is the process of changing a number from one numeral system (radix) to another. While humans primarily use Base-10 (Decimal) for daily life, computers operate using Base-2 (Binary), and developers often use Base-16 (Hexadecimal) for memory addressing and color codes.
Common Number Systems
- Binary (Base 2): Uses only 0 and 1. The foundation of digital computing.
- Octal (Base 8): Uses digits 0-7. Used in older computing systems and Unix file permissions.
- Decimal (Base 10): The standard system using digits 0-9.
- Hexadecimal (Base 16): Uses 0-9 and letters A-F to represent values 10-15.
How to Convert Bases Manually
1. Converting to Decimal (The Expansion Method)
To convert any base to decimal, multiply each digit by the base raised to the power of its position (starting from 0 on the right).
= (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)
= 8 + 4 + 0 + 1 = 13₁₀
2. Converting from Decimal (The Remainder Method)
To convert from decimal to another base, repeatedly divide the number by the target base and track the remainders.
13 ÷ 2 = 6, Remainder 1
6 ÷ 2 = 3, Remainder 0
3 ÷ 2 = 1, Remainder 1
1 ÷ 2 = 0, Remainder 1
Read bottom to top: 1101₂
Why Use Our Base Converter?
Our tool supports custom radices from 2 to 36. It handles complex conversions between non-decimal bases by utilizing a Decimal intermediary, ensuring high precision. Whether you are a student learning computer science or a professional debugging hex dumps, our simulator provides instant, accurate results.