By Vadim Vasyukevich

This ebook is devoted to new mathematical tools assigned for logical modeling of the reminiscence of electronic units. The for instance 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 good judgment. In a sort of the corresponding equations, they organically healthy analytical expressions of Boolean algebra. hence, a type of symbiosis is shaped utilizing parts of asynchronous sequential common sense at the one hand and combinational common sense nonetheless. So, asynchronous common sense is represented within the kind of greater Boolean good judgment. The booklet includes preliminary recommendations, primary definitions, statements, ideas and ideas wanted for theoretical justification of the mathematical equipment and its validity for asynchronous common sense. Asynchronous operators named venjunctor and sequentor are designed for sensible implementation. those simple parts are assigned for figuring out of reminiscence capabilities in sequential circuits. current study paintings is the ultimate degree of generalization and systematization of all these principles and investigations, author’s curiosity to which alternately flashed up and pale over a long time and for numerous purposes until eventually shaped “critical mass”, and all findings have been prepared definitively as a mathematical foundation of a idea thoroughly linked less than a standard subject matter – asynchronous sequential common sense, 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 (1st Edition)**

**Sample text**

Remark on Intersection of Sets All elements of sequention are arranged in a certain order, and this circumstance must be taken into account when operation of intersection is performed. That is because a nonempty intersection of unordered sets, {x ∩ y} = {z} as example, not in the least exclude the possibility of empty intersection of the corresponding sequentions: 〈x〉 ∩ 〈y〉 = ∅. Such a discrepancy might take place when the same elements of {z} set are included in sequentions 〈x〉 and 〈y〉 so that their orders differ from each other.

Sequention uniquely takes a zero value, if at least one of variables is reduced to zero. 1 Definition of Sequention Sequention is a function which takes 1 or 0 value depending on the values of binary arguments-variables as well as on the switching order of these variables. It is assumed that proposed binary operation of sequention is realized by a binary variable z as follows: z = F (〈x〉). 6) In view of the above-mentioned principles of sequention functioning, let us define that the corresponding logic obeys the following rules.

3). Each of these circuits performs the operation of venjunction: Z = X ∠ Y . BC – bistable cell (see Sect. 1, Fig. 1) is a basic logical element for venjunctor implementation. From a structural redundancy and signals race standpoint, it can be determined that the logical circuit shown in Fig. 3b realizes functionality of venjunctor most efficiently. Venjunctor is a two-input logical device intended for implementing venjunctive function. Venjunctor as bistable V-element of asynchronous logic is displayed in Fig.