Switching algebra

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The switching algebra is a special form of the Boolean algebra with a two-valued carrier set . It is tailored to switch arrangements and serves as an aid for calculating binary switching networks and switching mechanisms . It forms the logical framework for representing switching functions . In switching algebra, the term binary refers to the two switch states open and closed.

Switching algebra is isomorphic to propositional logic . This is why the typical propositional logic terms and operator names are used in it, and the term “logic” often denotes the technical elements used (e.g. logic gates ).

development

Switching algebra was mainly founded by Claude Shannon in his master's thesis A Symbolic Analysis of Relay and Switching Circuits from 1937. Today, a distinction is seldom made between switching algebra and Boolean algebra because they are almost the same from a mathematical point of view. The only difference is the choice of terminology , since the switching algebra is expressly used to describe the relationships between the states of the switches inside a switching arrangement. For a consideration of the logical aspect of switching algebra, the reader is referred to the article on Boolean algebra .

application

The switching networks, which are calculated with the help of switching algebra, were previously mainly produced using relay technology or similar electromechanical designs. As a rule, the switch state “off” is assigned a logical zero, the switch state “on” a logical one. From a logical point of view, this assignment is arbitrary and can also be reversed.

In today's digital technology , binary switching systems are mainly built up from electronic components. The logical states are realized by different voltages .

Areas of responsibility

Multi-valued switching algebra

Based on the multivalued logic , you can also define multivalued switching algebras. In particular, there is a lot of theoretical work on ternary switching algebra. However, this is of little practical importance, since ternary digital circuits cannot be produced effectively at the moment.

See also

literature

  • Dieter Bär: Introduction to switching algebra . Verlag Technik, Berlin 1967.

Web links

Wikibooks: Digital circuit technology  - learning and teaching materials