Easily convert numbers between different bases (binary, decimal, octal, hexadecimal). All conversions are performed in your browser - no data is sent to any server.
Conversion
Frequently Asked Questions
What is a numeral system?
A numeral system is a method for expressing numbers. The system we use in everyday life is the decimal system (base 10), which uses 10 digits from 0 to 9. Other common systems include binary (base 2, using only 0 and 1), octal (base 8, using digits from 0 to 7), and hexadecimal (base 16, using digits from 0 to 9 and letters A to F).
Why use different number bases?
Different number bases are used for various reasons:
• Binary (base 2): Used by computers because they operate with electronic circuits that have two states (on/off). It's the fundamental base in computing.
• Octal (base 8): Historically used in computing because it allows representing 3 binary bits in a single digit. While less common today, it's still used in contexts like Unix file permissions.
• Decimal (base 10): Our standard system, likely adopted because humans have ten fingers. It's intuitive for most people.
• Hexadecimal (base 16): Commonly used in programming as it allows representing 4 binary bits in a single character, making binary values easier to read. It's often used for memory addresses, CSS colors, etc.
How are hexadecimal numbers represented?
The hexadecimal system (base 16) uses 16 symbols: digits from 0 to 9 and letters A to F (or a to f, case-insensitive) to represent values from 10 to 15. For example:
• Decimal 10 is represented as 'A' in hexadecimal
• Decimal 11 is represented as 'B' in hexadecimal
• Decimal 15 is represented as 'F' in hexadecimal
• Decimal 26 is represented as '1A' in hexadecimal (1 × 16 + 10)
In programming, hexadecimal numbers are often prefixed with "0x" (like 0x1A) to distinguish them from decimal numbers.
Can you show me some examples of base conversions?
Here are some common base conversion examples:
• Decimal to Binary: 42 (base 10) → 101010 (base 2)
• Binary to Decimal: 1101 (base 2) → 13 (base 10)
• Hexadecimal to Decimal: 2F (base 16) → 47 (base 10)
• Decimal to Hexadecimal: 255 (base 10) → FF (base 16)
• Octal to Binary: 17 (base 8) → 1111 (base 2)
• Binary to Hexadecimal: 11111111 (base 2) → FF (base 16)
What are the limitations of this tool?
This tool supports positive integers of any size (using JavaScript's BigInt). It does not support negative numbers or floating-point numbers. For very large numbers, conversion might take slightly longer, but remains instantaneous for most common uses.
Is my data secure when using this tool?
Yes, all conversions are performed entirely in your browser. Your data never leaves your device and is not sent to any server. This tool uses JavaScript running locally in your browser to perform the conversions, ensuring complete privacy.