Unit Conversion

Base Converter

Convert numbers between binary, octal, decimal, hexadecimal, and any custom base from 2 to 36, with fractional parts and steps.

Interactive Base Converter

Convert integers and fractional values between binary, octal, decimal, hexadecimal, and custom bases (2 to 36) in real-time.

Real-Time Conversion Grid

Type a value into any input field below. The converter will instantly calculate and update the corresponding values in all other bases.

Custom Base Radix:
Base 2 Base 36

Radix Converter (Custom Base to Base)

Convert a specific number from any base directly to another base, showing detailed division and multiplication steps.

Examples:

Tip: Place your cursor inside the input field above, then click these buttons to insert high-radix digits.

Character Radix Reference Table (A to Z values)

Positional values: 0-9 represent themselves; A represents 10, B represents 11, up to Z which represents 35.

Step-by-Step Mathematical Explanation

Enter a value in the Radix Converter above to see step-by-step conversion steps.

What is a Number Base (Radix)?

A number base or radix is the number of unique digits (including zero) used to represent numbers in a positional numeral system. The most common system is the decimal system (base 10), which uses ten digits from 0 to 9.

In computing and digital systems, other bases are widely used:

  • Binary (Base 2): Uses only 0 and 1. It is the fundamental language of computer processors.
  • Octal (Base 8): Uses digits 0 to 7. Often used in Unix file permissions.
  • Hexadecimal (Base 16): Uses digits 0 to 9 and letters A to F. It provides a human-friendly shortcut for representing binary data (each hex digit represents exactly 4 bits).
  • Custom Bases (2 to 36): Any system using digits 0 to 9 and letters A to Z (for values up to 35).

Expert Tips & Best Practices

  • Bases are also called radixes. Base 2 is binary, base 8 is octal, base 10 is decimal, and base 16 is hexadecimal.
  • Digits above 9 are represented by letters (e.g., A=10, B=11, ..., Z=35). This convention supports bases up to 36.
  • When converting fractional numbers (like 0.1), some fractions that terminate in one base may repeat infinitely in another (e.g., 0.1 in decimal is 0.0001100110011... in binary).

Frequently Asked Questions

What is a number base?
A base (or radix) is the number of unique digits, including zero, that a system uses to represent numbers.
How do you represent values greater than 9 in bases larger than 10?
In bases greater than 10, letters from the Latin alphabet are used. A represents 10, B represents 11, C represents 12, up to Z which represents 35 in base 36.
Can the base converter handle decimal points?
Yes, this converter supports fractional parts (numbers with decimal points) for all bases between 2 and 36, showing how the fractional math converts.
What is the Base Converter?
The Base Converter is an online Unit Conversion calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Base Converter?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.