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Switching circuit theory is the mathematical study of the properties of networks of idealized switches. Such networks may be strictly combinational logic, in which their output state is only a function of the present state of their inputs; or may also contain sequential elements, where the present state depends on the present state and past states; in that sense, sequential circuits are said to include "memory" of past states. An important class of sequential circuits are state machines. Switching circuit theory is applicable to the design of telephone systems, computers, and similar systems. Switching circuit theory provided the mathematical foundations and tools for digital system design in almost all areas of modern technology. In an 1886 letter,
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...
described how logical operations could be carried out by electrical switching circuits. During 1880–1881 he showed that NOR gates alone (or alternatively NAND gates alone) can be used to reproduce the functions of all the other
logic gate A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for ...
s, but this work remained unpublished until 1933. The first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called
Sheffer stroke In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, ...
; the
logical NOR In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (''p'' NOR ''q'') is true precisely when neither ''p' ...
is sometimes called ''Peirce's arrow''. Consequently, these gates are sometimes called ''universal logic gates''. In 1898, Martin Boda described a switching theory for signalling block systems. Eventually,
vacuum tube A vacuum tube, electron tube, thermionic valve (British usage), or tube (North America) is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. It ...
s replaced relays for logic operations.
Lee De Forest #REDIRECT Lee de Forest {{redirect category shell, {{R from move{{R from other capitalisation ...
's modification, in 1907, of the
Fleming valve The Fleming valve, also called the Fleming oscillation valve, was a thermionic valve or vacuum tube invented in 1904 by English physicist John Ambrose Fleming as a detector for early radio receivers used in electromagnetic wireless telegrap ...
can be used as a logic gate.
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Witt ...
introduced a version of the 16-row
truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arg ...
as proposition 5.101 of ''
Tractatus Logico-Philosophicus The ''Tractatus Logico-Philosophicus'' (widely abbreviated and Citation, cited as TLP) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal ...
'' (1921). Walther Bothe, inventor of the coincidence circuit, got part of the 1954
Nobel Prize The Nobel Prizes ( ; ; ) are awards administered by the Nobel Foundation and granted in accordance with the principle of "for the greatest benefit to humankind". The prizes were first awarded in 1901, marking the fifth anniversary of Alfred N ...
in physics, for the first modern electronic AND gate in 1924.
Konrad Zuse Konrad Ernst Otto Zuse (; ; 22 June 1910 – 18 December 1995) was a German civil engineer, List of pioneers in computer science, pioneering computer scientist, inventor and businessman. His greatest achievement was the world's first programm ...
designed and built electromechanical logic gates for his computer Z1 (from 1935 to 1938). The theory was independently established through the works of NEC engineer Akira Nakashima in Japan,
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...
in the United States, and Victor Shestakov in the Soviet Union. The three published a series of papers showing that the two-valued Boolean algebra, can describe the operation of switching circuits. However, Shannon's work has largely overshadowed the other two, and despite some scholars arguing the similarities of Nakashima's work to Shannon's, their approaches and theoretical frameworks were markedly different. Also implausible is that Shestakov's influenced the other two due to the language barriers and the relative obscurity of his work abroad. Furthermore, Shannon and Shestakov defended their theses the same year in 1938, and Shestakov did not publish until 1941. Ideal switches are considered as having only two exclusive states, for example, open or closed. In some analysis, the state of a switch can be considered to have no influence on the output of the system and is designated as a "don't care" state. In complex networks it is necessary to also account for the finite switching time of physical switches; where two or more different paths in a network may affect the output, these delays may result in a "logic hazard" or "
race condition A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events, leading to unexpected or inconsistent ...
" where the output state changes due to the different propagation times through the network.


See also

* Circuit switching * Message switching *
Packet switching In telecommunications, packet switching is a method of grouping Data (computing), data into short messages in fixed format, i.e. ''network packet, packets,'' that are transmitted over a digital Telecommunications network, network. Packets consi ...
*
Fast packet switching In telecommunications, fast packet switching is a variant of packet switching In telecommunications, packet switching is a method of grouping Data (computing), data into short messages in fixed format, i.e. ''network packet, packets,'' that are ...
*
Network switching subsystem Network switching subsystem (NSS) (or GSM core network) is the component of a GSM system that carries out call out and mobility management functions for mobile phones roaming on the network of base stations. It is owned and deployed by mobi ...
* 5ESS Switching System * Number One Electronic Switching System *
Boolean circuit In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible inpu ...
* C-element *
Circuit complexity In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related notion is the circui ...
* Circuit minimization *
Karnaugh map A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which itself was a rediscovery of ...
* Logic design *
Logic gate A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for ...
*
Logic in computer science Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas: * Theoretical foundations and analysis * Use of computer technology to aid logicians ...
* Nonblocking minimal spanning switch *
Programmable logic controller A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing processes, such as assembly lines, machines, robotic devices, or any activity that ...
– computer software mimics relay circuits for industrial applications * Quine–McCluskey algorithm *
Relay A relay Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts An automotive-style miniature relay with the dust cover taken off A relay is an electrically operated switc ...
– an early kind of logic device * Switching lemma * Unate function


References


Further reading

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(2+xx+556+2 pages) * (xviii+686 pages) * (188 pages) * (4+60 pages) * (xviii+212 pages) {{Digital electronics Circuit complexity Digital circuits Digital electronics