Binary Converter
Convert numbers between binary, decimal, hexadecimal, and octal number systems.
Frequently Asked Questions
What is binary and why do computers use it?
Binary is a base-2 number system using only 0 and 1. Computers use binary because digital circuits operate in two states: on (1) and off (0), corresponding to high and low voltage. Every piece of data — text, images, video — is ultimately stored and processed as a sequence of binary digits (bits). The simplicity of two states makes electronic circuits reliable and efficient. Groups of 8 bits form a byte, which can represent 256 different values (0–255).
How do I convert decimal to binary?
To convert a decimal number to binary, repeatedly divide by 2 and record the remainders from bottom to top. For example, converting 13: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1. Reading remainders upward gives 1101. You can verify by calculating: 1×8 + 1×4 + 0×2 + 1×1 = 13. This process works for any positive integer and is fundamental to understanding how data is represented inside every computer, smartphone, and digital device.
What is hexadecimal and when is it used?
Hexadecimal (base-16) uses digits 0–9 and letters A–F (representing 10–15). It provides a compact way to represent binary data since one hex digit equals exactly four binary bits. For example, binary 11111111 = hex FF = decimal 255. Hexadecimal is widely used in programming, web colors (#FF5733), memory addresses, and debugging because it's much shorter than binary while still having a direct relationship to the underlying bits. Programmers often prefer hex over decimal for low-level data inspection.