Binary numeral system

Binary is a numeral system with base 2. It uses only two symbols: 0 and 1. Each symbol is called a bit.

Like the decimal system, the value of each symbol depends on its position. Each position to the left is doubled. For example, 1011 in binary means 8 + 0 + 2 + 1, which equals 11 in decimal.

Conversion method

A decimal number is converted to binary by repeatedly dividing by 2 and recording the remainders. Reading the remainders from bottom to top gives the binary number. The reverse conversion is done by multiplying the value of each position by the appropriate power of 2, then adding the results.

Arithmetic

Binary addition follows simple rules: 0+0=0, 0+1=1, 1+1=0 with a carry to the next position. Multiplication and subtraction follow similar principles, but manual calculation becomes lengthy as numbers grow larger.

Use in technology

Computers and digital devices store and transmit data using two states, such as the presence or absence of electric current, or the direction of rotation. This makes the binary system the foundation for designing logic circuits. All stored data—text, images, and sound—ultimately appears as a sequence of bits.

History and related systems

The idea of a numeral system based on two values emerged in mathematics and philosophy before modern computers. The German mathematician Gottfried Wilhelm Leibniz was among those who documented the system. Other systems using powers of 2, such as octal and hexadecimal, are also used to write binary numbers compactly.