What is a number base converter?

A number base converter is a tool that converts numbers between different number systems (bases), such as binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each base uses a different set of digits and place values.

What are the common number bases?

The most common number bases are: Binary (base 2, uses 0-1), Octal (base 8, uses 0-7), Decimal (base 10, uses 0-9), and Hexadecimal (base 16, uses 0-9 and A-F).

How do I convert between number bases?

Enter your number in the input field, select the source base (binary, octal, decimal, or hexadecimal), and the converter will automatically show the equivalent in all other bases. The conversion happens in real-time.

What is hexadecimal used for?

Hexadecimal (base 16) is commonly used in computing and programming because it's a compact way to represent binary data. Each hexadecimal digit represents 4 bits, making it easy to work with binary data.

Can I convert negative numbers or decimals?

This converter supports positive integers. For negative numbers and decimals, you would need to handle the sign and fractional parts separately, which is more complex.

Is the number base converter free to use?

Yes, completely free! No registration, no limits, no hidden fees. All conversions happen in your browser - we never see or store your data.

🔢 Number Base Converter

Convert numbers between different number systems: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Free online number base converter with real-time conversion.

From Base

Uses digits 0-9

To Base

Uses digits 0-9, A-F

Auto-convert (real-time)

Quick Examples:

Input (Decimal)

Uses digits 0-9. Prefix none is optional.

Common Number Conversions

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
2	10	2	2
8	1000	10	8
10	1010	12	A
16	10000	20	10
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400

What is a Number Base?

A number base (also called radix) is the number of unique digits, including zero, used to represent numbers in a positional numeral system. The most common number base is 10 (decimal), which we use in everyday life. However, computers and programming languages often use different bases like binary (base 2), octal (base 8), and hexadecimal (base 16).

Each position in a number represents a power of the base. For example, in decimal (base 10), the number 123 represents (1 × 10²) + (2 × 10¹) + (3 × 10⁰) = 100 + 20 + 3 = 123.

Number Systems Explained

Binary (Base 2)

Uses only two digits: 0 and 1. This is the fundamental number system used by computers.

Example: 1010 in binary = 10 in decimal

Prefix: 0b or 0B

Octal (Base 8)

Uses digits 0 through 7. Less common but still used in some Unix file permissions.

Example: 755 in octal = 493 in decimal

Prefix: 0o or 0O

Decimal (Base 10)

Uses digits 0 through 9. This is the standard number system we use in daily life.

Example: 42 in decimal = 42

Prefix: None

Hexadecimal (Base 16)

Uses digits 0-9 and letters A-F (or a-f). Very common in programming and web development for colors and memory addresses.

Example: FF in hexadecimal = 255 in decimal

Prefix: 0x or 0X

Common Use Cases

Programming: Converting between number bases is essential in programming, especially when working with bitwise operations, memory addresses, or color codes.

Web Development: Hexadecimal is commonly used for CSS color codes (e.g., #FF5733 for colors).

Computer Science: Understanding binary is fundamental to understanding how computers work at the lowest level.

File Permissions: Unix/Linux file permissions are often represented in octal (e.g., 755, 644).

Debugging: When debugging programs, you may need to convert between bases to understand memory dumps or error codes.

Networking: IP addresses and network configurations sometimes use different number bases.

Conversion Examples

Decimal to Binary

To convert 42 from decimal to binary:

42 ÷ 2 = 21 remainder 0
21 ÷ 2 = 10 remainder 1
10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 101010
So 42 (decimal) = 101010 (binary)

Binary to Hexadecimal

To convert 101010 from binary to hexadecimal:

Group binary digits into groups of 4 from right:
101010 → 0010 1010

Convert each group:
0010 = 2 (decimal) = 2 (hex)
1010 = 10 (decimal) = A (hex)

So 101010 (binary) = 2A (hexadecimal)

Hexadecimal to Decimal

To convert FF from hexadecimal to decimal:

F = 15 (decimal)
FF = (15 × 16¹) + (15 × 16⁰)
   = (15 × 16) + (15 × 1)
   = 240 + 15
   = 255

So FF (hexadecimal) = 255 (decimal)

Tips for Using Number Base Converter

✓Prefixes: You can include prefixes (0x, 0b, 0o) in your input, or omit them. The converter will automatically detect and handle them.
✓Case Sensitivity: Hexadecimal letters (A-F) are case-insensitive. The converter will automatically uppercase the output.
✓Whitespace: Spaces in your input will be automatically removed during conversion.
✓Validation: The converter validates input according to the selected base to ensure accurate conversions.
✓Real-time: Enable auto-convert for instant conversion as you type, or disable it for manual control.
✓Swap: Use the swap button to quickly exchange the input and output bases.