Number Base Converter

Convert between decimal, binary, octal, and hexadecimal

Use the fields below to calculate results or convert units for this tool.

Input Number

Input Base

Decimal (Base 10)

Enter a valid number

Binary (Base 2)

0bEnter a valid number

Octal (Base 8)

0oEnter a valid number

Hexadecimal (Base 16)

0xEnter a valid number

Common Number Conversions

Decimal	Binary	Octal	Hexadecimal
0	0b0	0o0	0x0
1	0b1	0o1	0x1
8	0b1000	0o10	0x8
16	0b10000	0o20	0x10
32	0b100000	0o40	0x20
64	0b1000000	0o100	0x40
128	0b10000000	0o200	0x80
255	0b11111111	0o377	0xFF

Number Base Systems

Decimal (Base 10): Uses digits 0-9

Binary (Base 2): Uses digits 0-1

Octal (Base 8): Uses digits 0-7

Hexadecimal (Base 16): Uses digits 0-9, A-F

Common Use Cases

Binary: Computer systems, digital logic

Octal: Unix file permissions, legacy systems

Hexadecimal: Colors, memory addresses, debugging

Decimal: Human-readable numbers, calculations

About Number Base Conversion

Convert numbers between different base systems including decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Essential for computer science, programming, digital electronics, and mathematics. Our converter provides instant, accurate conversions with validation.

Number Base Applications

Computer programming and debugging
Digital electronics and logic design
Memory address calculations
Color codes and web development

Frequently Asked Questions

What is the difference between number bases?

Number bases represent how many digits are used in counting: decimal (base 10) uses 0-9, binary (base 2) uses 0-1, octal (base 8) uses 0-7, and hexadecimal (base 16) uses 0-9 and A-F.

Why do computers use binary?

Computers use binary because digital circuits have two states: on (1) and off (0). This matches perfectly with binary's two digits, making it the natural choice for digital electronics and computer processing.

When is hexadecimal used in programming?

Hexadecimal is used for memory addresses, color codes (#FF0000 for red), debugging, and representing binary data compactly. One hex digit represents exactly 4 binary digits, making conversions straightforward.

What is octal used for?

Octal is commonly used in Unix/Linux file permissions (chmod 755), some programming contexts, and legacy computer systems. Each octal digit represents exactly 3 binary digits.

How do I convert between bases manually?

To convert from any base to decimal, multiply each digit by the base raised to its position power. To convert from decimal to another base, repeatedly divide by the target base and collect remainders.

What are the prefixes for different number bases?

Common prefixes include: 0b for binary (0b1010), 0o for octal (0o755), 0x for hexadecimal (0xFF). These prefixes help identify the number base in programming languages and technical documentation.