DOC

Base Converter

Convert numbers between Binary, Octal, Decimal, and Hexadecimal

Tool Overview

The Base Converter is a powerful tool for converting numbers between four commonly used number systems: Binary, Octal, Decimal, and Hexadecimal. Simply enter a number in any base, and the tool will automatically convert it to all other bases in real-time.

Go to Tool

Number Bases Explained

Binary (Base 2)

Binary uses only two digits: 0 and 1. It is the fundamental language of computers, where each digit (bit) represents an electrical state (off or on). Binary numbers are prefixed with 0b.

0b1010 = 10 (decimal)

Octal (Base 8)

Octal uses digits from 0 to 7. It was widely used in early computing as a compact representation of binary (3 bits = 1 octal digit). Octal numbers are prefixed with 0 or 0o.

012 = 10 (decimal)

Decimal (Base 10)

Decimal uses digits from 0 to 9. It is the most common number system used by humans, based on the ten fingers. Decimal numbers have no prefix.

10 = 10 (decimal)

Hexadecimal (Base 16)

Hexadecimal uses digits from 0 to 9 and letters A to F (representing 10-15). It is widely used in programming for representing colors, memory addresses, and binary data. Hexadecimal numbers are prefixed with 0x.

0xA = 10 (decimal)

Conversion Table

Decimal | Binary | Octal | Hex ---------|----------|-------|----- 0 | 0 | 0 | 0 1 | 1 | 1 | 1 2 | 10 | 2 | 2 3 | 11 | 3 | 3 4 | 100 | 4 | 4 5 | 101 | 5 | 5 6 | 110 | 6 | 6 7 | 111 | 7 | 7 8 | 1000 | 10 | 8 9 | 1001 | 11 | 9 10 | 1010 | 12 | A 15 | 1111 | 17 | F 16 | 10000 | 20 | 10 255 | 11111111 | 377 | FF

Features

  • Real-time conversion between all four number bases
  • Support for Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16)
  • Input validation for each base
  • Clear button for each input field
  • Responsive design
  • Offline support

Usage Examples

Example 1: Convert Decimal to Binary

Input (Decimal): 255

Output:

  • Binary: 11111111
  • Octal: 377
  • Hexadecimal: FF

Example 2: Convert Hexadecimal to Decimal

Input (Hexadecimal): 1A3

Output:

  • Binary: 110100011
  • Octal: 643
  • Decimal: 419

Example 3: Convert Binary to Hexadecimal

Input (Binary): 10101010

Output:

  • Octal: 252
  • Decimal: 170
  • Hexadecimal: AA

FAQ

What is a number base?

A number base (or radix) is the number of unique digits used to represent numbers. For example, base 10 uses 10 digits (0-9), while base 2 uses only 2 digits (0-1).

Why is hexadecimal used in programming?

Hexadecimal is compact and easy to convert to binary (each hex digit = 4 bits). It's commonly used for memory addresses, color codes, and binary data representation.

Can I convert negative numbers?

Currently, the Base Converter supports only non-negative integers. For negative numbers, you would need to use two's complement representation.

What is the maximum number I can convert?

The tool uses JavaScript's Number type, which can accurately represent integers up to 2^53 - 1 (approximately 9 quadrillion). For larger numbers, precision may be lost.