Two-element Boolean algebra
The Boolean algebra is a special form of Boolean algebra with a divalent support amount. It is designed for switching arrangements and serves as a tool to calculate binary and sequential circuits works. The term binary refers to the switching algebra on the two switch states opened and closed.
The Boolean algebra is isomorphic to propositional logic. Therefore, in her the typical terms and Operator name of propositional logic are used and the term " logic " often denotes the mathematical and technical elements used (eg, logic gates ).
Development
The Boolean algebra was justified mainly by Claude Shannon in his Master's thesis A Symbolic Analysis of Relay and Switching Circuits by 1937. Today is between switching algebra and Boolean algebra rarely distinguished, since they are virtually the same from a mathematical point of view. Only in the choice of terminology differences may exist because the switching algebra is explicitly used to describe the relationships between the states of the switches inside a switch assembly. For the consideration of the logical aspect of the Boolean algebra, the reader is therefore referred to the article on Boolean algebra.
Application
The switching networks, which are calculated by using the Boolean algebra, were formerly manufactured mainly in relay technology or similar electro- mechanical designs. Typically in this case the switch "off" state is assigned to a logical zero, the switch is "on " according to a logical one. This assignment is arbitrary, from a logical point of view, and can also be reversed.
In today's digital technology to build binary switching systems predominantly from electronic components. Here, the logic states are realized by different voltage levels. Normally enter the higher level means the logical one and the lower level of the logical zero (see logic level ).
Areas of responsibility
- Description of switching functions by "logical" Terme
- Provision of computational rules of Boolean algebra
- Equivalent transformation of terms
- Normal form theory
- Minimization of terms
Multivalued Switching Algebra
Based on the multi-valued logic can also define multi-valued Schaltalgebren. There are especially a lot of theoretical work on the ternary switching algebra. However, this has practically no importance, as currently ternary digital circuits technically can not be effectively made .