This tool converts numbers between four common numerical bases: Decimal (base 10), Binary (base 2), Octal (base 8), and Hexadecimal (base 16). Enter a number in any base to see its equivalent value in all other bases.
Formula Used
Value (Base A) → Decimal (Base 10) → Value (Base B)
Decimal (Base 10)
— standard human number system using digits 0-9
Binary (Base 2)
— computer system using digits 0 and 1
Octal (Base 8)
— system using digits 0-7, representing groups of 3 bits
Hexadecimal (Base 16)
— system using digits 0-9 and letters A-F, representing groups of 4 bits
Example Calculation
If you enter the Decimal number 42, the converter translates it: Binary = 101010; Octal = 52; Hexadecimal = 2A. All fields update simultaneously.
Frequently Asked Questions
A number base is the number of unique digits used to represent numbers. Decimal is base 10 (10 digits). Binary is base 2 (2 digits). Hexadecimal is base 16 (16 digits, adding letters A-F).
Computers use binary because digital hardware uses transistors that operate in one of two states: ON (represented as 1) or OFF (represented as 0).
Hexadecimal is used in computing to represent binary data in a more human-readable format. Since one hex digit represents exactly 4 binary bits, a byte (8 bits) can be written as just two hex digits.
Multiply each binary digit by its place value (powers of 2) starting from the right (2⁰, 2¹, 2², etc.) and sum the results. For example, 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10.
This simple base converter is designed for integers. Converting fractions between bases can result in repeating decimals depending on the base.