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Number Base Converter

Convert numbers between binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and any custom base up to 36.

Binary

Base 2

Octal

Base 8

Decimal

Base 10

Hexadecimal

Base 16

Custom Base

What is Number Base Converter?

A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. Decimal (base 10) uses digits 0–9, binary (base 2) uses 0–1, octal (base 8) uses 0–7, and hexadecimal (base 16) uses 0–9 and A–F. This converter handles all four standard bases plus any custom base from 2 to 36, using letters A–Z for digit values 10–35.

How to use

  1. 1 Enter a number in any of the four fields — binary, octal, decimal, or hexadecimal.
  2. 2 All other fields update instantly with the equivalent value.
  3. 3 Use the custom base fields to convert to/from any base between 2 and 36.
  4. 4 For hexadecimal, letters A–F are case-insensitive.

Formula

To convert from base N to decimal: multiply each digit by N raised to its positional power and sum the results. To convert from decimal to base N: repeatedly divide by N and collect remainders in reverse order.

Example calculation

Binary 1101 → Decimal: 1×8 + 1×4 + 0×2 + 1×1 = 13. Decimal 13 → Octal: 13÷8=1 R5 → 15. Decimal 13 → Hex: D.

Frequently asked questions

Why do computers use binary?

Binary maps directly to the two physical states of electronic components: on (1) and off (0). Logic gates, memory cells, and transistors all operate in these two states, making binary the natural language of digital hardware.

What is hexadecimal used for?

Hexadecimal is a compact representation of binary — each hex digit exactly represents 4 binary bits. It is used in programming, memory addresses, color codes (e.g. #FF5733), machine code, and debugging because it is far more readable than long binary strings.

What is octal used for?

Octal (base 8) groups binary into sets of 3 bits. It was commonly used in older computing systems and is still seen in Unix/Linux file permissions (e.g. chmod 755).

What is the highest base this converter supports?

Base 36, which uses digits 0–9 and letters A–Z. Base 36 is sometimes used for compact URL-safe identifiers and case-insensitive encoding.

Can I convert negative numbers?

This calculator converts unsigned (non-negative) integers. For negative numbers in binary, two's complement representation is required, which depends on the bit width and is beyond the scope of a simple base converter.