Switching circuit theory

This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (November 2014) (Learn how and when to remove this template message)

Switching circuit theory is the mathematical study of the properties of networks of idealized switches. Such networks may be strictly

In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits.^[2] 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NAND gates alone) can be used to reproduce the functions of all the other logic gates, but this work remained unpublished until 1933.^[3] The first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Sheffer stroke; the logical NOR is sometimes called Peirce's arrow.^[4] Consequently, these gates are sometimes called universal logic gates.^[5]

In 1898, Martin Boda described a switching theory for signalling block systems.^[6][7]

Eventually,

From 1934 to 1936, NEC engineer Akira Nakashima,^[8] Claude Shannon^[9] and Victor Shestakov^[10] published a series of papers showing that the two-valued Boolean algebra, which they discovered independently, can describe the operation of switching circuits.^{[7][11][12][13][1]}

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" where the output state changes due to the different propagation times through the network.

See also

• Circuit switching
• Message switching
• Packet switching
• Fast packet switching
• Network switching subsystem
• 5ESS Switching System
• Number One Electronic Switching System
• Boolean circuit
• C-element
• Circuit complexity
• Circuit minimization
• Karnaugh map
• Logic design
• Logic gate
• Logic in computer science
• Nonblocking minimal spanning switch
• Programmable logic controller – computer software mimics relay circuits for industrial applications
• Quine–McCluskey algorithm
• Relay – an early kind of logic device
• Switching lemma
• Unate function

References