binaires

Binaires refers to the base-2 numeral system and to data representations that use two symbols, typically 0 and 1. In mathematics as well as computer science, binaires provide a simple, two-state framework to encode quantities, instructions, and signals. Each position in a binary number represents a power of two, with the rightmost digit representing 2^0.

The concept has ancient precursors, but the modern treatment of binary as a place-value system was developed in the 17th century by Gottfried Wilhelm Leibniz, who connected it to philosophical ideas and demonstrated arithmetic operations in base 2. The system is favored in computing because a two-state medium—such as electrical on/off states, transistors, or magnetic domains—allows reliable representation and manipulation of data.

In practice, a single binary digit is called a bit; eight bits form a byte. Larger groups are organized into bytes, words, and memory blocks. Binary arithmetic follows standard rules with carries propagating as in decimal addition. Signed numbers are commonly represented using two's complement. Binary fractions use fixed-point or floating-point formats to represent real numbers.

Binaires underpin digital computers, data storage, and communication. Text, images, and sounds are encoded into binary through character encodings (such as ASCII or Unicode), color channels in images, and samples in audio. Logical operations on bits, including AND, OR, and XOR, form the basis of computer algorithms and digital circuits.