Binära

Binära (binary) is the base-2 numeral system that uses two symbols, 0 and 1. The term binära is used in Swedish and other languages to describe binary concepts. In mathematics and computer science, sequences of binary digits, or bits, are used to represent numbers, text, and instructions.

History: The concept appeared in various ancient numeral systems, but the modern binary system was developed and popularized by Gottfried Wilhelm Leibniz in the 17th century; he linked binary to philosophical ideas of truth and falsity. Binary arithmetic can be performed with basic addition rules using carries.

Representation: A binary number is written as a sequence of bits; each position represents a power of two. Example: 1101_2 equals 13 in decimal. A byte consists of eight bits; leading zeros do not change value.

Applications: Electronic computers use binary because two stable states (on/off) are easy to implement with transistors. Binary encodes data via various schemes such as ASCII and UTF-8; programming relies on binary logic and Boolean algebra.

Related concepts: octal and hexadecimal provide compact representations; binary data can be interpreted as signed integers using two's complement; error-checking codes and data compression rely on binary operations.