Base Converter
Convert numbers between different number systems and bases
Number Base Converter
Supports integers and decimals. Use A-Z for digits above 9.
Conversion Results
Enter a number and select bases to see the conversion
Base Conversion Reference
| Decimal | Binary | Octal | Hexadecimal | Base 36 |
|---|
Understanding Number Systems
Positional Notation
Number systems use positional notation where the position of each digit determines its value. Each position represents a power of the base.
Example: Decimal 1234
- • 1 × 10³ = 1000
- • 2 × 10² = 200
- • 3 × 10¹ = 30
- • 4 × 10⁰ = 4
- • Total = 1234
Common Number Bases
Different bases are used for various applications in mathematics, computer science, and everyday life.
Base Applications
- • Binary (2): Computer systems
- • Octal (8): Unix file permissions
- • Decimal (10): Everyday counting
- • Hexadecimal (16): Memory addresses
- • Base 60: Time and angles
Number System Properties
Binary (Base 2)
Uses only digits 0 and 1. Fundamental to digital computers and electronics.
Octal (Base 8)
Uses digits 0-7. Often used in computing as a shorthand for binary.
Decimal (Base 10)
Standard human counting system using digits 0-9.
Hexadecimal (Base 16)
Uses digits 0-9 and letters A-F. Common in computer programming.
Base 36
Uses digits 0-9 and letters A-Z. Maximum base using standard alphanumeric characters.
Custom Bases
Any base from 2 to 36 can be used for specialized applications.
Conversion Methods
- • Division method for integer parts
- • Multiplication method for fractions
- • Direct substitution for small numbers
- • Grouping method for binary/octal/hex
- • Polynomial expansion method
- • Successive division algorithm
Practical Applications
- • Computer programming and debugging
- • Digital circuit design
- • Cryptography and encoding
- • Memory address calculations
- • Color codes in web design
- • Data compression algorithms
Mathematical Properties
- • All bases represent same numbers
- • Base affects representation length
- • Lower bases need more digits
- • Powers of 2 bases relate to binary
- • Base conversion preserves value
- • Arithmetic rules apply universally
Related Calculators
Binary Calculator
Perform arithmetic operations in binary
Scientific Calculator
Advanced mathematical calculations
Programmer Calculator
Bitwise operations and number system tools