Base Converter

Base Converter - Convert Numbers Between Different Number Systems

This powerful base converter allows you to convert numbers between any number base from 2 to 36. Whether you're working with binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), or any other number system, this tool provides instant conversions with detailed calculation steps.

What is a number base?

A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. For example:
- Base 2 (binary): uses digits 0 and 1
- Base 8 (octal): uses digits 0-7
- Base 10 (decimal): uses digits 0-9
- Base 16 (hexadecimal): uses digits 0-9 and letters A-F
- Base 36: uses digits 0-9 and letters A-Z

How do I convert between different bases?

The conversion process involves two main steps:

1. Convert from source base to decimal (base 10):
- Multiply each digit by the base raised to the power of its position
- Sum all the results

2. Convert from decimal to target base:
- Divide the decimal number by the target base
- Record the remainder as the rightmost digit
- Repeat with the quotient until it becomes 0
- The result is the remainders read from bottom to top

What are the most common number bases used?

The most commonly used number bases are:

- Base 2 (Binary): Used in computer systems and digital electronics
- Base 8 (Octal): Sometimes used in computing, especially in Unix file permissions
- Base 10 (Decimal): The standard number system used in everyday life
- Base 16 (Hexadecimal): Widely used in computing and programming for representing memory addresses, colors, and binary data
- Base 64: Used for encoding binary data in text format (like Base64 encoding)

Can I convert numbers with decimal points?

This converter currently handles whole numbers (integers) only. For numbers with decimal points, the conversion process becomes more complex as it involves fractional parts. The integer part is converted using the standard method, while the fractional part requires multiplying by the target base and taking the integer part of the result repeatedly.

What happens with negative numbers?

This converter supports negative numbers. The conversion process works the same way, but the negative sign is preserved in the result. For example, -15 in decimal becomes -F in hexadecimal and -1111 in binary.

Why are there 36 different bases supported?

Base 36 is the largest base that can be represented using the digits 0-9 and letters A-Z (10 + 26 = 36 characters). This provides a good balance between the number of supported bases and the readability of the results. Higher bases would require additional symbols, making them less practical for most applications.

Common Number Base Reference