Number Base Converter
This tool converts numbers between different numeral systems, such as binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and higher bases like base 32. It helps you translate the same numeric value into representations that are commonly used in programming, networking, and low-level systems work.
By showing both a direct conversion and a set of common base representations, the tool makes it easy to verify results, compare formats, and understand how a value is expressed across systems without doing manual calculations.
How Base Conversion Works
Base conversion first interprets the input number according to its specified base, turning it into an internal numeric value. Each digit is validated to ensure it is legal for that base before the conversion proceeds.
Once interpreted, the value is re-encoded into the target base by repeatedly dividing by the output base and mapping remainders to the appropriate digit symbols. The result represents the same numeric quantity, just expressed using a different radix.
- Only integer values are supported
- Digits must be valid for the selected input base
Inputs and Options Explained
The inputs closely mirror how base conversion is described in textbooks and programming APIs, while options control how values are parsed and displayed.
- Input base — The base used to interpret the input number.
- Input number — The numeric value to convert, written using digits valid for the input base.
- Output base — The base to convert the value into.
- Uppercase output — Displays alphabetic digits (such as A–F) in uppercase.
- Ignore spaces & underscores — Allows visual separators in the input without affecting the value.
- Group digits — Groups digits in the output for easier reading.
Examples and Edge Cases
A value like 1010_1100 is valid binary input when separators are ignored, but the same characters would be invalid in decimal. The tool validates digits before converting to prevent silent errors.
Large values may produce long outputs in smaller bases, such as binary. Grouping digits can improve readability without changing the underlying value.
Who Should Use This Tool
This tool is useful whenever numeric values need to be translated between representations.
- Developers working with low-level data or encodings
- Students learning about number systems
- Engineers debugging binary or hexadecimal values
- Anyone verifying base conversions quickly
Related Concepts
Base conversion is a fundamental concept underlying many areas of computing.
- Radix notation — The base used to represent numbers.
- Positional numeral systems — Systems where digit position determines value.
- Binary encoding — Representing data using base 2.
When converted values are embedded in structured data, viewing them with the JSON Formatter can improve clarity. For generating identifiers or fingerprints rather than numeric representations, the UUID Generator & Validator or the Hash Generator may be more appropriate.