Master computer science mathematics. Instantly translate integers between Decimal, Binary, Hexadecimal, and Octal numerical systems.
Decimal (base 10)
255
Binary (base 2)
0b11111111
Octal (base 8)
0o377
Hexadecimal (base 16)
0xFF
Base 36
73
Base 64 (integer)
D/
Stop performing tedious long division on paper. Input any value and instantly see the equivalent across all computing architectures.
Unlike basic calculators, this tool does not require dropdown menus. Typing a value into any field immediately updates all the other mathematical bases in real-time.
The UI prevents impossible inputs. It blocks you from typing a `2` into the Binary field, or typing a `G` into the Hexadecimal field, ensuring your math never crashes.
Easily copy raw hexadecimal formats directly to your clipboard for use in defining CSS colors (like `#FFFFFF`) or specifying memory addresses in C++.
A 'Number Base' (or Radix) is simply the number of unique digits a mathematical system uses to represent numbers. As humans, we use a Decimal (Base-10) system because we evolved with ten fingers. We count from 0 to 9, and then combine those digits to make larger numbers. Computers, however, operate on entirely different physical constraints.
A computer's CPU does not have ten fingers. It is a piece of silicon filled with microscopic electrical switches. A switch can only be in one of two physical states: Electricity On, or Electricity Off.
Therefore, all hardware architecture relies on a Base-2 (Binary) system. It only has two digits: 0 and 1. Every photo you view, every song you stream, and every piece of software you use is ultimately translated into a massive sequence of zeroes and ones so the physical CPU can process it.
If computers use Binary, why do programmers use Hexadecimal?
Binary is extremely inefficient for humans to read. The number 255 in Decimal requires eight digits in Binary (11111111). If a developer needs to write a memory address or a color code, writing out massive strings of 1s and 0s guarantees a typo will occur.
Hexadecimal (Base-16) solves this by using sixteen digits: 0-9, and the letters A-F. Hex is magical because exactly four binary digits (a 'nibble') perfectly map to exactly one Hexadecimal character. The binary string 11111111 shrinks beautifully into the Hex string FF. An online base converter is essential for translating these architectural mappings.
While Hexadecimal dominates modern computing, you will still encounter Base-8 (Octal) in legacy systems—most notably in Unix/Linux file permissions.
chmod 755 file.txt, they are using Octal numbers to set the read, write, and execute bits for the file. The '7' translates to 111 in binary, granting all three permissions.In most programming languages (like JavaScript or Python), you can write different bases directly into the source code by using prefixes. 0b1010 tells the compiler the number is Binary. 0xFF tells the compiler the number is Hexadecimal. 0o755 tells the compiler the number is Octal.