Number System Converter
Convert between binary, decimal, hexadecimal, and octal number systems instantly
All Bases Conversion
| Binary (Base 2) | Octal (Base 8) | Decimal (Base 10) | Hexadecimal (Base 16) |
|---|---|---|---|
| - | - | - | - |
About Number System Conversion
Number system conversion is fundamental in computer science, digital electronics, and programming. Our free online converter helps you translate numbers between different bases instantly, with clear step-by-step explanations of the conversion process.
Number Systems Explained
Binary (Base 2)
Uses only two digits: 0 and 1. This is the fundamental language of computers, where each binary digit (bit) represents an on (1) or off (0) state in digital circuits.
Example: 10102 = 1010
Octal (Base 8)
Uses digits from 0 to 7. While less common today, octal was historically used in computing because it's easier to convert to binary than decimal.
Example: 128 = 1010
Decimal (Base 10)
The standard number system using digits 0-9. This is the system humans use in everyday life for counting and arithmetic.
Example: 1010 = A16
Hexadecimal (Base 16)
Uses digits 0-9 and letters A-F (representing 10-15). Widely used in programming and digital systems because it's more compact than binary and easy to convert.
Example: A16 = 10102
How to Use This Converter
- Enter your number in the input field
- Select the current base of your number (binary, decimal, etc.)
- Choose the target base you want to convert to
- Click "Convert" or enable "Auto Convert" for live results
- View the conversion result and detailed steps
- Use the "Copy" button to save your result
Common Use Cases
- Programming: Convert memory addresses between hex and binary
- Digital Electronics: Work with binary representations of circuits
- Computer Science: Understand how data is stored and processed
- Networking: Convert IP addresses between different formats
- Education: Learn number system concepts with step-by-step explanations
Frequently Asked Questions
Why is hexadecimal used in programming?
Hexadecimal is compact (one hex digit represents four binary digits) and easy to convert to/from binary, making it ideal for representing memory addresses, color codes, and other low-level data.
How accurate are the conversions?
Our conversions are mathematically precise. For very large numbers (beyond 64-bit), precision may be limited by JavaScript's number representation.
Can I convert negative numbers?
Currently, the tool supports conversion of positive integers only. Negative numbers would require understanding signed number representations like two's complement.
Is this tool free to use?
Yes, our number system converter is completely free with no limitations. You can convert as many numbers as you need without registration.