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A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with a radix of 2 .
Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra . Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in computer science , truth value ...
The name is a portmanteau of binary digit. [1] The bit represents a logical state with one of two possible values . These values are most commonly represented as either " 1 " or " 0 " , but other representations such as true / false , yes / no , on / off , or + / − are also widely used.
In particular, if b is a positive integer, then the unit is the amount of information that can be stored in a system with b possible states. When b is 2, the unit is the shannon, equal to the information content of one "bit" (a portmanteau of binary digit [2]). A system with 8 possible states, for example, can store up to log 2 8 = 3 bits of ...
A binary clock might use LEDs to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional sexagesimal time.. The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. [27]
The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" (hex), number format. In the decimal system, there are 10 digits, 0 ...
One early calculating machine, built entirely from wood by Thomas Fowler in 1840, operated in balanced ternary. [4] [5] [3] The first modern, electronic ternary computer, Setun, was built in 1958 in the Soviet Union at the Moscow State University by Nikolay Brusentsov, [6] [7] and it had notable advantages over the binary computers that eventually replaced it, such as lower electricity ...