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Avtomat. i Telemekh., 1959, Volume 20, Issue 7, Pages 898–907 (Mi at12783)  

This article is cited in 2 scientific papers (total in 2 papers)

Analysis and synthesis of certain electric circuits by means of special logical operators

A. D. Talantsev

Moscow

Abstract: An algebraic theory of the logical operation of some electric circuits is developed. This theory takes into account the time behaviour of circuit processes. The logical variable $Z$ when represented in the form of voltage-state signal is called «potential variable» denoted as $X$ and is called «pulse variable» denoted as $Y$ when represented in the form of pulse signal. The special logical operators are defined as follows. If at the moment of time $t$ a true value of variable $Z$ goes to a false value it is expressed by $dZ(t)=1$ and $dZ(t)=0$ is assumed in all other cases. The symbol $d$ is called «transition operator». The operator $D$ is defined by the formula (1). These operators describe changes of Boolean functions when their arguments change. Some of their properties are investigated (2)–(6).
Applying operators $d$ and $D$ to elementary function $\vee$ and & we obtain relationships (7)–(10). Applying operator $d$ to an arbitrary function of $n$ variables we obtain the formula (11). These relationships are outside the province of Boolean algebra. The new logical operators may be employed to characterize the behaviour of certain electric circuits called «homogeneous potential-pulse circuits. Transformation procedure for such circuits is developed.
The application of new operators to the design of certain digital control circuits is illustrated by an actual example.

Full text: PDF file (1470 kB)

Document Type: Article
Received: 01.11.1958

Citation: A. D. Talantsev, “Analysis and synthesis of certain electric circuits by means of special logical operators”, Avtomat. i Telemekh., 20:7 (1959), 898–907

Citation in format AMSBIB
\Bibitem{1}
\by A.~D.~Talantsev
\paper Analysis and synthesis of certain electric circuits by means of special logical operators
\jour Avtomat. i Telemekh.
\yr 1959
\vol 20
\issue 7
\pages 898--907
\mathnet{http://mi.mathnet.ru/at12783}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zaitseva E., Levashenko V., Kostolny J., “Importance Analysis Based on Logical Differential Calculus and Binary Decision Diagram”, Reliab. Eng. Syst. Saf., 138 (2015), 135–144  crossref  isi
    2. Zaitseva E. Levashenko V. Kostolny J., “Application of Logical Differential Calculus and Binary Decision Diagramin Importance Analysis”, Eksploat. Niezawodn., 17:3 (2015), 379–388  crossref  isi
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