Download PDF by Vadim Vasyukevich: Asynchronous Operators of Sequential Logic: Venjunction &

By Vadim Vasyukevich

ISBN-10: 3642216102

ISBN-13: 9783642216107

This e-book is devoted to new mathematical tools assigned for logical modeling of the reminiscence of electronic units. The working example is logic-dynamical operation named venjunction and venjunctive functionality in addition to sequention and sequentional functionality. Venjunction and sequention function in the framework of sequential common sense. In a sort of the corresponding equations, they organically healthy analytical expressions of Boolean algebra. therefore, a kind of symbiosis is shaped utilizing components of asynchronous sequential common sense at the one hand and combinational common sense nevertheless. So, asynchronous common sense is represented within the type of more desirable Boolean good judgment. The e-book includes preliminary thoughts, primary definitions, statements, rules and ideas wanted for theoretical justification of the mathematical gear and its validity for asynchronous common sense. Asynchronous operators named venjunctor and sequentor are designed for sensible implementation. those simple components are assigned for knowing of reminiscence capabilities in sequential circuits. current examine paintings is the ultimate level of generalization and systematization of all these principles and investigations, author’s curiosity to which alternately flashed up and pale over decades and for numerous purposes until eventually shaped “critical mass”, and all findings have been prepared definitively as a mathematical foundation of a conception safely linked lower than a standard subject matter – asynchronous sequential good judgment, primarily labeled as switching common sense, which falls into class of algebraic logics.

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Additional info for Asynchronous Operators of Sequential Logic: Venjunction & Sequention: Digital Circuit Analysis and Design

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2 A cyclic graph represents venjunctive functions on sequences of input switchings. Here, just as input sets, output values are also placed in graph nodes. For example, according to arc marked by asterisk “*” in Fig. 3a output value changes from 1 to 0 in the course of the switching x = 1/0 on the background y = 0. Graph edges allow transitions in both directions. For example, edge marked in Fig. 3b characterizes switchings y = 0/1 and y = 1/0 on the background x = 1. These switchings do not change zero output z = 0.

But if the orders are in agreement, then 〈x〉 ∩ 〈y〉 = 〈z〉. Furthermore, if {x ∩ {y} = ∅, then surely – 〈x〉 ∩ 〈y〉 = ∅. 2 Sequention – Function The basic idea (key point) of conversion of sequentions into functions is to concretize an abstract status of elements. All elements are considered to be Boolean variables. As a result sequention 〈x1 x2 … xn〉 may be used as a format for generating the corresponding set of binary sequences. 2 Sequention – Function 45 the manner of sequences of binary elements-variables.

It is a sort of graphic copy of a truth table for venjunction (see Sect. 5) looking like a cube with six cycles. 1) y) ∨ ( x ∠ y ) ∨ x ∧ y . 2) are displayed in Fig. 3. a) b) 11 1 10 1 01 0 11 1 10 0 11 0 01 1 11 0 00 1 10 1 * * 00 0 01 0 10 1 00 0 01 0 00 1 Fig. 3 Cyclic graphs of venjunctive functions: a) Eq. 1, b) Eq. 2 A cyclic graph represents venjunctive functions on sequences of input switchings. Here, just as input sets, output values are also placed in graph nodes. For example, according to arc marked by asterisk “*” in Fig.

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Asynchronous Operators of Sequential Logic: Venjunction & Sequention: Digital Circuit Analysis and Design by Vadim Vasyukevich


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