Number System Converter
Advanced number system converter for software development, computer science, and digital electronics. Handles binary, decimal, hexadecimal, and octal conversions with detailed explanations and real-world examples.
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Common Applications
Web Development
- Color Codes (Hex): #FF0000 = RGB(255,0,0)
- Unicode Characters: U+0041 = 65 (ASCII 'A')
- CSS Values: 255 = FF (opacity)
System Programming
- File Permissions: 644 (octal) = rw-r--r--
- Memory Addresses: 0xFF = 255 (offset)
- Binary Flags: 1010 = 10 (settings)
Technical Reference
| Base | Digits | Example | Usage | Common Values |
|---|---|---|---|---|
| Binary (2) | 0-1 | 1010 | Digital Logic | 8-bit: 00-FF |
| Decimal (10) | 0-9 | 255 | Standard Math | 0-255 (byte) |
| Hex (16) | 0-9, A-F | FF | Memory/Colors | #RRGGBB |
| Octal (8) | 0-7 | 644 | File Permissions | rwx (Unix) |
Understanding Number Systems
Binary (Base-2)
Core computing number system:
- Uses only 0 and 1
- Each bit position = power of 2
- Example: 1010 = 10 decimal
Decimal (Base-10)
Our standard counting system:
- Uses digits 0-9
- Each position is power of 10
- Used in everyday calculations
- Natural for human counting
- Example: 255 = FF (hex)
Hexadecimal (Base-16)
Common in programming:
- Uses 0-9 and A-F
- Each digit = 4 binary digits
- Memory addresses
- Color codes (#FF0000)
- Example: FF = 255 (decimal)
Octal (Base-8)
Used in specific contexts:
- Uses digits 0-7
- Each digit = 3 binary digits
- Unix file permissions
- Legacy systems
- Example: 377 = 255 (decimal)
Frequently Asked Questions
To convert decimal to binary, select "Decimal (Base 10)" as your input format and "Binary (Base 2)" as your output format. Enter your decimal number and the conversion will happen automatically.
Hexadecimal (Base-16) is a number system that uses 16 digits: 0-9 and A-F. It's commonly used in programming for representing memory addresses, color codes (like #FF0000 for red), and making binary numbers more readable.
Binary is a base-2 number system that only uses two digits: 0 and 1. This matches how computers work internally, where each digit represents an electronic signal that's either on (1) or off (0). Any number can be represented using just these two digits.
Decimal (Base-10) uses digits 0-9 and is our standard counting system. Octal (Base-8) only uses digits 0-7. While decimal is used in everyday counting, octal is sometimes used in computing and programming, particularly in file permissions on Unix-like systems.
You can verify your conversion by converting the result back to the original number system - it should match your input. Our tool also provides examples of common conversions in the table below the converter for reference.
While our converter can handle most common numbers, very large numbers might be limited by JavaScript's number precision limits. For practical purposes, numbers up to 2^53 (9007199254740991) can be converted accurately.