Base Converter
Convert numbers between different bases (binary, octal, decimal, hexadecimal, etc.). Essential for computer science, programming, digital electronics, and understanding number systems.
Convert Number Base
Convert numbers between different number systems:
Any Base → Decimal → Target Base
Example: 1010₂ = 10₁₀ = A₁₆
Understanding Number Systems
Number systems (bases) are fundamental to computer science and digital systems. Each base uses a different set of digits and represents values differently, which is crucial for understanding how computers process and store information.
Common Number Bases
🔢 Binary (Base 2)
Digits: 0, 1
Used in: Digital electronics, computer memory
Example: 1010₂ = 10₁₀
All computer data is ultimately binary
📊 Octal (Base 8)
Digits: 0-7
Used in: Older computer systems, file permissions
Example: 77₈ = 63₁₀
Groups 3 binary digits together
🔟 Decimal (Base 10)
Digits: 0-9
Used in: Everyday counting, human communication
Example: 42₁₀ = 42₁₀
Most familiar number system
💻 Hexadecimal (Base 16)
Digits: 0-9, A-F
Used in: Memory addresses, color codes, programming
Example: FF₁₆ = 255₁₀
Groups 4 binary digits together
Computer Science Applications
💾 Memory Addresses
Hexadecimal for RAM and ROM addresses
Easier to read than long binary strings
Memory debugging and programming
Pointer arithmetic in C/C++
🎨 Color Codes
RGB color values: #FF0000 = Red
HTML/CSS color specifications
Image processing and graphics
Digital art and design tools
🔐 Cryptography
Large prime numbers in different bases
Hash function representations
Public key cryptography
Digital signature algorithms
🌐 Network Addresses
MAC addresses in hexadecimal
IP address conversions
Network packet analysis
Protocol debugging
Digital Electronics
⚡ Logic Circuits
Binary representation of digital signals
Truth tables and Boolean algebra
Digital circuit design
FPGA programming
💽 Data Storage
Binary encoding of all digital data
File system structures
Database indexing
Data compression algorithms
🔌 Communication Protocols
Serial data transmission
Modem signal encoding
Wireless communication
Data packet formatting
🎮 Game Development
Sprite and texture coordinates
Color palette management
Audio sample encoding
Game state representation
Programming and Software
🐍 Python & Programming
Binary literals: 0b1010
Hex literals: 0xFF
Octal literals: 0o77
Base conversion functions
☕ JavaScript
parseInt(value, base) for conversion
toString(base) for output
Binary: 0b, Octal: 0o, Hex: 0x
ES6 number literal support
⚙️ Assembly Language
Direct binary and hex manipulation
Memory address calculations
Bit manipulation operations
Low-level system programming
🗃️ Database Systems
Binary data storage
Hash index calculations
UUID generation
Checksum algorithms
Base Conversion Examples
| Decimal | Binary | Octal | Hexadecimal | Common Use |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | Null/Zero value |
| 1 | 1 | 1 | 1 | Single bit/Unit |
| 10 | 1010 | 12 | A | Line feed (ASCII) |
| 16 | 10000 | 20 | 10 | Word boundary |
| 32 | 100000 | 40 | 20 | Space character |
| 64 | 1000000 | 100 | 40 | @ symbol (ASCII) |
| 128 | 10000000 | 200 | 80 | € symbol (Latin-1) |
| 255 | 11111111 | 377 | FF | Maximum byte value |
💻 Computer Science Tip: Understanding different number bases is essential for programming and computer science. Binary is the foundation of all digital computing, while hexadecimal provides a more human-readable way to work with binary data. Most programming languages support base conversion functions.
Historical Development
🏛️ Ancient Systems
Babylonian base-60 (sexagesimal)
Egyptian hieroglyphic numerals
Roman numeral system
Mayan base-20 (vigesimal)
Chinese counting rods
📚 Positional Notation
Indian decimal system development
Zero concept introduction
Arabic numeral adoption
Place value understanding
Modern decimal dominance
⚙️ Computing Era
Binary system adoption
Octal for early computers
Hexadecimal standardization
Unicode and character encoding
Modern computing foundations
Advanced Applications
🔬 Scientific Computing
Arbitrary precision arithmetic
Floating-point representation
Scientific notation
Complex number systems
Mathematical modeling
🎵 Digital Audio
Sample rate representations
Bit depth calculations
Audio compression algorithms
Frequency domain analysis
Sound wave digitization
📺 Digital Video
Resolution calculations
Color depth analysis
Compression ratios
Frame rate conversions
Video encoding standards
🌐 Internet Protocols
IP address calculations
Subnet mask operations
Port number assignments
Protocol header analysis
Network packet inspection