Binary Number Converter
Convert between different number systems: binary, decimal, hexadecimal, and octal
Different number systems are used in computing and mathematics. Here are the main ones:
- Binary (Base-2): Uses only 0 and 1, fundamental to computer systems
- Decimal (Base-10): Standard system using digits 0-9
- Hexadecimal (Base-16): Uses 0-9 and A-F, common in programming
- Octal (Base-8): Uses digits 0-7, used in some computing contexts
The conversion process involves these steps:
- Identify the source number system
- Convert to decimal as an intermediate step
- Convert from decimal to the target system
Common conversions:
- Binary to Decimal: 1010₂ = 10₁₀
- Decimal to Hex: 255₁₀ = FF₁₆
- Hex to Binary: FF₁₆ = 11111111₂
- Octal to Decimal: 10₈ = 8₁₀
Number system conversions are essential in:
- Computer programming and software development
- Digital electronics and hardware design
- Network administration (IP addresses, subnet masks)
- Color coding (RGB values in hexadecimal)
- Memory addressing and debugging
- File permissions in Unix/Linux systems
Real-world examples of number system usage:
- Web Colors: #FF0000 (hexadecimal) for pure red
- File Permissions: 755 (octal) for read/write/execute settings
- Memory Addresses: 0x1A2B3C4D (hexadecimal) in debugging
- Binary Data: 10101010 for digital signal processing
Q: Why do computers use binary?
A: Computers use binary because electronic circuits can easily represent two states (on/off, high/low voltage), making binary the most reliable and efficient system for digital processing.
Q: When is hexadecimal used instead of binary?
A: Hexadecimal is used when binary numbers would be too long to read easily. Since each hexadecimal digit represents 4 binary digits, it's more compact and readable for humans while maintaining a direct relationship with binary.
Q: What's the advantage of the octal system?
A: Octal is historically used in computing because it's easier to convert between binary and octal than decimal, and it was particularly useful in early computing systems. Today, it's still used in Unix file permissions and some legacy systems.