Number Base Converter
Convert numbers between binary, decimal, octal, and hexadecimal instantly. Free developer tool with real-time updates.
Common Conversions
Tip
Hexadecimal numbers are commonly used for color codes (FF = 255 = max white)
Number Base Converter: Binary, Decimal, Hex, Octal
Convert numbers instantly between binary (base 2), decimal (base 10), octal (base 8), and hexadecimal (base 16). Essential for developers, computer science students, and anyone working with digital systems.
Number base conversion is fundamental in programming and electronics. Our tool performs all conversions simultaneously and in real-time, directly in your browser.
How to Use
- Enter a number in any field (decimal, binary, octal, or hexadecimal)
- Other fields update automatically in real-time
- Click the copy button to grab any value
Reference Table
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
Use Cases
💻 Programming
Quickly convert memory addresses, bit masks, hexadecimal color codes.
🎓 Education
Check your number base conversion exercises.
🔌 Electronics
Work with registers, data buses, and addressing codes.
🎨 Web Design
Convert RGB values to hexadecimal for CSS colors.
Why Use This Converter?
⚡ Real-time
All conversions update instantly as you type.
🔄 Multi-directional
Enter in any field, others update automatically.
🔒 100% Local
Calculations run in your browser. No data sent anywhere.
🎯 Accurate
Exact conversions for all integers up to 2^53.
📋 Quick Copy
Copy any converted value with one click.
✅ Validation
Automatic detection of invalid inputs for each base.
❓ Frequently Asked Questions (FAQ)
What's the difference between these number bases?
Each base uses a different number of symbols to represent values:
- Binary (base 2): 2 digits (0, 1) - used by computers
- Octal (base 8): 8 digits (0-7) - historically used in Unix
- Decimal (base 10): 10 digits (0-9) - our everyday system
- Hexadecimal (base 16): 16 symbols (0-9, A-F) - compact for developers
Why is hexadecimal so popular in programming?
Hexadecimal is popular because each hex digit corresponds exactly to 4 binary bits. This allows large binary values to be represented compactly and readably.
For example:
FFin hex =11111111in binary =255in decimal- A byte (8 bits) always writes as 2 hex digits
- CSS color codes (#FFFFFF) use hex (2 digits per RGB component)
Are negative numbers supported?
This tool converts positive integers. In computing, negative numbers are represented using two's complement, which depends on register size (8, 16, 32, 64 bits). This representation isn't universal and is outside the scope of this simple tool.
What's the size limit for numbers?
Conversions are accurate up to 2^53 - 1 (9,007,199,254,740,991), the "safe integer" limit in JavaScript (Number.MAX_SAFE_INTEGER).
Beyond this, rounding errors may occur due to double-precision floating-point representation (IEEE 754).
How do I manually convert binary to decimal?
To convert 1010 (binary) to decimal:
1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10
Each position represents a power of 2, starting with 2⁰ on the right.