Number Base Converter
Convert between decimal, binary, hexadecimal, and octal number systems.
Example: 42, 255, 1000
Example: 101010, 11111111
Example: 2A, FF, 3E8
Example: 52, 377, 1750
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About Number Base Conversion
What is a Number Base?
Number bases (or numeral systems) are ways to represent numbers using a specific set of digits. The most common is decimal (base 10) which uses digits 0-9, but other bases are important in computing.
Common Number Bases
- Decimal (Base 10): Uses digits 0-9
- Binary (Base 2): Uses only 0 and 1
- Hexadecimal (Base 16): Uses 0-9 and A-F
- Octal (Base 8): Uses digits 0-7
Common Use Cases
- Computer programming and low-level system operations
- Understanding memory addresses (typically in hexadecimal)
- Network configurations and IP addressing
- Color representation in web development (hexadecimal)
- Binary data analysis and manipulation
- Computer science education and algorithm development
How to Use
Enter a number in any of the input fields, and the tool will automatically convert it to all other number bases. The tool validates input based on the selected base.
Frequently Asked Questions
What number bases does this converter support?
The converter supports the most commonly used number bases: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). These cover the vast majority of programming and mathematical applications.
How do I convert a number from one base to another?
Simply enter your number in any of the input fields (binary, octal, decimal, or hexadecimal), and the tool will automatically calculate and display the equivalent values in all other bases. The conversion happens instantly as you type.
What is the difference between these number systems?
Binary (base 2) uses only 0 and 1, commonly used in computer science. Octal (base 8) uses digits 0-7. Decimal (base 10) is our everyday counting system using digits 0-9. Hexadecimal (base 16) uses digits 0-9 and letters A-F.
Why would I need to convert between number bases?
Base conversion is essential in programming, computer science, and digital electronics. You might need to convert decimal numbers to binary for bit operations, use hexadecimal for memory addresses, or work with octal for file permissions in Unix systems.
What are the valid characters for each number base?
Binary: 0, 1 only. Octal: 0-7 only. Decimal: 0-9 only. Hexadecimal: 0-9 and A-F (or a-f). The tool will automatically validate your input and show an error if you enter invalid characters for the selected base.
Can I convert negative numbers?
Yes, the tool supports negative numbers. However, note that different systems may represent negative numbers differently (sign-magnitude, one's complement, two's complement), so the results show the mathematical conversion rather than specific encoding methods.
Is there a limit to the size of numbers I can convert?
The tool can handle very large numbers, but extremely large values may hit JavaScript's number precision limits. For most practical applications in programming and mathematics, the supported range is more than sufficient.
How do I verify that my conversion is correct?
You can verify conversions by converting back to the original base or by using the mathematical definition of each base. For example, binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal.
What does the "A-F" mean in hexadecimal?
Hexadecimal uses 16 symbols, so after the digits 0-9, it continues with letters A-F representing values 10-15. So A=10, B=11, C=12, D=13, E=14, F=15. This allows representation of any value from 0-15 in a single digit.
Can I use this tool for learning number systems?
Absolutely! This tool is perfect for students learning about different number bases. You can experiment with different values to see how they translate between systems and develop an intuition for base conversion.
How does octal relate to binary?
Octal and binary have a special relationship: each octal digit represents exactly 3 binary digits. This makes conversion between octal and binary particularly straightforward, which is why octal was historically popular in computing.
Why is hexadecimal so common in programming?
Hexadecimal is popular because it's a compact way to represent binary data. Each hex digit represents exactly 4 binary digits, making it much easier to read and write than long strings of 0s and 1s, especially for memory addresses and color codes.