Base Calculator

Common Bases

• Binary (Base 2): Uses digits 0-1. Foundation of digital computing
• Octal (Base 8): Uses digits 0-7. Common in computing
• Decimal (Base 10): Uses digits 0-9. Standard human counting
• Hexadecimal (Base 16): Uses 0-9, A-F. Common in programming

How It Works

• Each position represents a power of the base
• Rightmost position is base⁰ = 1
• Next position is base¹
• And so on, moving left

Example: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀

Programming

• Color codes (hex)
• Memory addresses
• Bit manipulation
• File permissions (octal)

Computing

• IP addresses
• Binary operations
• Character encoding
• Data representation

Education

• Number theory
• Computer science
• Digital electronics
• Mathematics