Number Base Converter

Convert numbers between binary, octal, decimal, hexadecimal, and any custom base from 2 to 36. Type in any field to see live conversions with step-by-step work.

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How It Works

Every positional number system works the same way: each digit's value depends on its position. In base b, the rightmost digit is multiplied by b⁰ = 1, the next by b¹, then b², and so on.

To convert from any base to decimal: multiply each digit by the base raised to its position power, then sum all values. For example, 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2&sup0; = 8 + 0 + 2 + 1 = 11.

To convert from decimal to any base: repeatedly divide by the target base and collect the remainders in reverse order. For example, 11 ÷ 2 = 5 r 1, 5 ÷ 2 = 2 r 1, 2 ÷ 2 = 1 r 0, 1 ÷ 2 = 0 r 1 → reading remainders bottom-up gives 1011₂.

Number Systems

• Decimal (Base 10): The standard number system we use daily. Uses digits 0-9.
• Binary (Base 2): Computer's native language. Only uses 0 and 1.
• Octal (Base 8): Uses digits 0-7. Common in Unix file permissions.
• Hexadecimal (Base 16): Uses 0-9 and A-F. Compact representation of binary — each hex digit represents 4 bits.

Common Uses

• Binary: Low-level programming, bitwise operations, computer architecture
• Octal: File permissions in Unix/Linux (e.g., chmod 755)
• Hexadecimal: Colors (#FF5733), memory addresses (0x1A2B), MAC addresses

Binary Bit Ranges

• 1 bit: 0 or 1
• 8 bits (1 byte): 0–255 unsigned, −128 to 127 signed
• 16 bits: 0–65,535 unsigned, −32,768 to 32,767 signed
• 32 bits: 0–4,294,967,295 unsigned, −2,147,483,648 to 2,147,483,647 signed

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Quick Reference

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