binarys

Binary is the base-2 numeral system that represents values using two symbols: 0 and 1. It is the standard numeral system of modern digital electronics and computer architectures. The concept has ancient roots in logical ideas and binary counting, but its formal development is credited to Gottfried Wilhelm Leibniz in the 17th century, who showed how arithmetic could be carried out using only two symbols.

In binary, each digit is a bit, a binary digit, occupying a place value that is a power of two. Reading from right to left, the bits correspond to 2^0, 2^1, 2^2, etc. For example, 1011 in binary equals 11 in decimal, since 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0 = 8 + 0 + 2 + 1 = 11. Binary also encodes fractions using digits after the binary point, with weights 2^-1, 2^-2, and so on.

Binary is central to computing. Digital circuits use two distinct voltage levels to represent 0 and 1, enabling reliable logic operations. Data is stored and transmitted as sequences of bits; groups of eight bits form a byte, and larger structures encode text, images, and executable programs. Common encodings, such as ASCII or UTF-8, map characters to binary patterns. Error detection and correction schemes exploit binary representations to ensure data integrity.

Notes: The term binarys is nonstandard; the usual terms are binary, binaries, or binary numbers when referring to multiple representations.