Binary Converter

Repeatedly divide the decimal number by 2 and record the remainder (0 or 1) each time. Read the remainders from bottom to top to get the binary representation. For example, 10 ÷ 2 = 5 R0, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1. Reading up: 1010.

Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit is called a bit (binary digit). Groups of 8 bits form a byte. Binary is the foundation of all digital computing because electronic circuits naturally represent two states: off (0) and on (1).

Every piece of data in a computer — text, images, video, programs — is ultimately stored and processed as binary. Processors execute machine code in binary, memory stores bits in billions of tiny transistors, and all arithmetic is performed with binary logic gates (AND, OR, NOT, XOR).

Two's complement is the most common way to represent negative integers in binary. To negate a number: invert all bits (one's complement) then add 1. For example, +5 in 8-bit is 00000101. Inverted: 11111010. +1 = 11111011, which is -5. This makes binary arithmetic consistent for both positive and negative numbers.