Numeral Base Converter
Convert integers between Decimal, Hexadecimal, Binary, Octal, and custom bases with arbitrary-precision math. 100% local calculation.
What are Positional Numeral Systems?
A **positional numeral system** is a method of representing numbers where the value of a digit depends on its position relative to the decimal point (or radix). The number of unique digits available in a system is called its **base** or **radix**.
The most popular bases used in technology and mathematics include:
- Decimal (Base 10): The standard system used by humans, originating from our ten fingers. It utilizes digits from 0 to 9.
- Binary (Base 2): The internal language of computers, using only 0 and 1. It represents transistor states of OFF and ON.
- Hexadecimal (Base 16): A compact way to write binary data. Since a single hex digit represents 4 bits, it is heavily used in memory addresses, color codes, and byte values. It uses digits 0-9 and letters A-F.
- Octal (Base 8): Formerly popular in mainframe computing, using digits 0-7. Each octal digit maps to precisely 3 bits.
Frequently Asked Questions
Base conversion translates a number from one positional numeral system to another. It parses a value using its input base rules (sum of digits multiplied by base powers), computes its underlying mathematical value, and formats it using the divisions/remainders of the output base.
This tool uses JavaScript BigInt arithmetic under the hood, enabling arbitrary-precision integer conversions. It can handle incredibly large numbers without rounding or losing mathematical precision.
Besides Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16), our tool lets you choose custom bases from 2 to 36. Bases larger than 10 use letters of the alphabet (A-Z) to represent digits from 10 to 35.