Number Base Converter

Convert numbers between number bases like binary, decimal, hexadecimal, octal, and more instantly. Free number base converter for computer science and programming.

Smart Tips

• Binary (base 2) uses only 0 and 1 - fundamental to computer systems

• Hexadecimal (base 16) uses 0-9 and A-F, often used for colors and memory addresses

• Octal (base 8) was historically used in computing but is less common today

• Each hex digit represents exactly 4 binary digits (bits)

The Formula

Decimal = Σ(digit × base^position)

digit = Each digit in the number
0 to (base-1)

base = Number base (2, 8, 10, 16, etc.)
Radix of the number system

position = Position from right (0-indexed)
Rightmost digit is position 0

Number Base Conversion Reference

Base	Description
Binary (Base 2)	Uses digits 0 and 1, fundamental in computing
Octal (Base 8)	Uses digits 0-7, common in Unix permissions
Decimal (Base 10)	Standard system using digits 0-9
Hexadecimal (Base 16)	Uses 0-9 and A-F, common in programming
Base 36	Uses 0-9 and A-Z, maximum for single character encoding

Key Insights

Base Systems

Different number bases (binary, octal, decimal, hexadecimal) use different digits and place values for representation.

Binary System

Binary (base-2) uses only 0 and 1, fundamental to computer science and digital electronics.

Hexadecimal System

Hexadecimal (base-16) uses 0-9 and A-F, commonly used in programming and memory addresses.

Practical Uses

Number base conversion is essential for programming, debugging, networking, and understanding computer systems.

Frequently Asked Questions

Number bases define how many digits are used in a number system. Decimal uses 10 digits (0-9), binary uses 2 digits (0-1), and hexadecimal uses 16 digits (0-9, A-F). Different bases are used in computing and mathematics.

To convert decimal to binary, repeatedly divide by 2 and collect remainders. To convert binary to decimal, multiply each digit by its place value (2^n) and sum the results. Our converter handles this automatically.

Hexadecimal (base-16) uses digits 0-9 and letters A-F. It's commonly used in computing because it's easy to convert to/from binary (4 binary digits = 1 hex digit) and represents large numbers compactly.

Our converter uses precise mathematical algorithms and provides accurate results for all supported number bases. All conversions maintain mathematical integrity and handle large numbers correctly.

We support decimal (base-10), binary (base-2), octal (base-8), hexadecimal (base-16), and other common number systems including ternary, quaternary, quinary, senary, septenary, nonary, duodecimal, vigesimal, and base 36. The converter handles conversions between any supported bases.

Our number base conversions are based on positional numeral system principles, base conversion algorithms, and computer science number representation standards.

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Converted Value

Enter values to convert

Note:Number base conversions use positional numeral system principles. Ensure the input digits are valid for the selected base. For critical applications, verify conversions manually.