🔢 How to Use
- Enter a number in any base (Binary, Octal, Decimal, or Hex)
- All other bases update automatically
- Click on quick reference examples to load them
- Share results using the toolbar buttons
🎯 Common Use Cases
💻 Programming
Convert between number systems for debugging and development
🎨 Color Codes
Convert hex color codes to RGB decimal values
🔐 Cryptography
Work with hexadecimal hash values
🎓 Education
Learn and understand different number systems
🔒 Privacy & Security
Your privacy is safe with us. All number system conversions are performed locally within your browser using client-side scripts. No numeric inputs or details are ever sent to our servers. Learn more in our Privacy Policy.
📖 Understanding Number Systems & Bases
A number system represents numbers using a consistent set of symbols. The total number of unique symbols or digits used by a system is called its base or radix. In modern computer science and software development, four primary bases are used:
Binary (Base 2)
Uses only 0 and 1. This matches the physical binary states of electric circuits (on/off) and is the fundamental language of all computers.
Octal (Base 8)
Uses digits 0 through 7. Grouping binary digits into triplets allows representation in octal, which is often used in Linux file permissions.
Decimal (Base 10)
Uses digits 0 through 9. This is the standard human-readable numbering system, likely developed due to humans having ten fingers.
Hexadecimal (Base 16)
Uses 0-9 and letters A-F to represent 10-15. Hex is highly compact; one hex character represents exactly 4 binary bits (a nibble).
Base Conversion Quick Reference Table
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 5 | 0101 | 5 | 5 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
Understanding Bits, Bytes, and Nibbles
A single binary digit (0 or 1) is a bit. Because a bit is too small to represent complex data, bits are grouped:
- Bit: The basic unit of data (0 or 1).
- Nibble (4 bits): Can represent values from 0 to 15. This maps perfectly to exactly one hexadecimal digit.
- Byte (8 bits): The standard unit of computer memory. Can hold values from 0 to 255. Two hexadecimal characters represent exactly one byte (e.g., 0xFF).
❓ FAQ
How do I convert binary to decimal? ▼
Simply enter your binary number (using only 0 and 1) in the Binary field, and the Decimal field will automatically show the converted value.
What is hexadecimal? ▼
Hexadecimal (hex) is a base-16 number system using digits 0-9 and letters A-F. It's commonly used in programming for colors (#FF0000), memory addresses, and more.
What's the relationship between these number systems? ▼
Binary (base-2) uses 2 digits (0-1), Octal (base-8) uses 8 digits (0-7), Decimal (base-10) uses 10 digits (0-9), and Hexadecimal (base-16) uses 16 digits (0-9, A-F).
Can I use prefixes like 0x for hex? ▼
Yes! The tool recognizes common prefixes: 0b for binary, 0o for octal, and 0x for hexadecimal, but they're optional.
Is my data private? ▼
Yes. All conversions happen entirely in your browser. Your data never leaves your device.