Binary numeral system in the context of "Digital electronic circuit"

Braille (/ˈbreɪl/ BRAYL, French: [bʁaj] ) is a tactile writing system used by blind or visually impaired people. It can be read either on embossed paper or by using refreshable braille displays that connect to computers and smartphone devices. Braille can be written using a slate and stylus, a braille writer, an electronic braille notetaker or with the use of a computer connected to a braille embosser. For blind readers, braille is an independent writing system, rather than a code of printed orthography.

Braille is named after its creator, Louis Braille, a Frenchman who lost his sight as a result of a childhood accident. In 1824, at the age of fifteen, he developed the braille code based on the French alphabet as an improvement on night writing. He published his system, which subsequently included musical notation, in 1829. The second revision, published in 1837, was the first binary form of writing developed in the modern era.

In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠${\displaystyle {\tfrac {p}{q}}}$⁠ of two integers, a numerator p and a non-zero denominator q. For example, ⁠${\displaystyle {\tfrac {3}{7}}}$⁠ is a rational number, as is every integer (for example, ${\displaystyle -5={\tfrac {-5}{1}}}$). The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also calledthe field of rationals or the field of rational numbers. It is usually denoted by boldface Q, or blackboard bold ⁠${\displaystyle \mathbb {Q} .}$⁠

A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: 3/4 = 0.75), or eventually begins to repeat the same finite sequence of digits over and over (example: 9/44 = 0.20454545...). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see Repeating decimal § Extension to other bases).

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 in mathematical logic and related domains and binary variable in statistics.

In computing, bit numbering is the convention used to identify the bit positions in a binary number. The bits can be those in a memory byte or word, or those of an internal CPU register or data bus.

A Post machine or Post–Turing machine is a "program formulation" of a type of Turing machine, comprising a variant of Emil Post's Turing-equivalent model of computation. Post's model and Turing's model, though very similar to one another, were developed independently. Turing's paper was received for publication in May 1936, followed by Post's in October. A Post–Turing machine uses a binary alphabet, an infinite sequence of binary storage locations, and a primitive programming language with instructions for bi-directional movement among the storage locations and alteration of their contents one at a time. The names "Post–Turing program" and "Post–Turing machine" were used by Martin Davis in 1973–1974 (Davis 1973, p. 69ff). Later in 1980, Davis used the name "Turing–Post program" (Davis, in Steen p. 241).

The RCA Mark II Sound Synthesizer (nicknamed Victor) was the first programmable electronic synthesizer and the flagship piece of equipment at the Columbia-Princeton Electronic Music Center. Designed by Herbert Belar and Harry Olson at RCA, with contributions by Vladimir Ussachevsky and Peter Mauzey, it was installed at Columbia University in 1957. Consisting of a room-sized array of interconnected sound synthesis components, the Mark II gave the user more flexibility and had twice the number of tone oscillators as its predecessor, the Mark I. The synthesizer was funded by a large grant from the Rockefeller Foundation.

Earlier 20th century electronic instruments such as the Telharmonium or the theremin were manually operated. The RCA combined diverse electronic sound generation with a music sequencer, which proved a huge attraction to composers of the day, who were growing weary of creating electronic works by splicing together individual sounds recorded on sections of magnetic tape. The RCA Mark II featured a binary sequencer using a paper tape reader analogous to a player piano, that would send instructions to the synthesizer, automating playback from the device. The synthesizer would then output sound to a synchronized record lathe next to the machine. The resulting recording would then be compared against the punch-tape score, and the process would be repeated until the desired results were obtained.