Asynchronous Operators of Sequential Logic: Venjunction & by Vadim Vasyukevich

By Vadim Vasyukevich

This booklet 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 kind of the corresponding equations, they organically healthy analytical expressions of Boolean algebra. therefore, a kind of symbiosis is shaped utilizing parts of asynchronous sequential common sense at the one hand and combinational common sense however. So, asynchronous good judgment is represented within the kind of improved Boolean common sense. The publication comprises preliminary recommendations, primary definitions, statements, rules and principles wanted for theoretical justification of the mathematical gear and its validity for asynchronous good judgment. Asynchronous operators named venjunctor and sequentor are designed for functional implementation. those uncomplicated components are assigned for knowing of reminiscence capabilities in sequential circuits. current learn paintings is the ultimate level of generalization and systematization of all these rules and investigations, author’s curiosity to which alternately flashed up and pale over a long time and for varied purposes till shaped “critical mass”, and all findings have been prepared definitively as a mathematical foundation of a conception thoroughly linked less than a standard subject matter – asynchronous sequential good judgment, primarily categorised as switching good judgment, which falls into class of algebraic logics.

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

Example text

2 follows that after replacement of logical NAND-elements (Fig. 1) with NOR-elements (Fig. 2) functioning of bistable cell changes in a certain way. 3 Bistable cell (Fig. 2) functioning: a) output ZX; b) output ZY. a) b) Y X 1 0/1 1/0 0 1 - 0 0 - 0/1 0 - - 0 1/0 1 - - 0 - 1 1 Y 1 0/1 1/0 0 1 - 0 1 - 0/1 0 - - 1 0 1/0 0 - - 1 - 0 - 0 0 - X Former logic operations and structure of formulae remain valid, but input and output signals are subject to negation. 1) Z Y = FY ( X , Y ) . 2) The corresponding changes have an effect on venjunctive expressions.

1) element x1 occupies the first position, x2 – the second, and so on until xn. Number “n” assigns a length of ordered sequence (number of elements), and therefore n-positioned sequention is specified as n-sequention. The set {x1 x2 … xn} does not contain similar, equal one to another elements. In other words sequention should not permit repeated elements. Every sequention is finite in length, and it incorporates initial (First) element xF = x1 and final (Last) element xL = xn in accordance with 〈x1 x2 … xn〉.

It is obvious that venjunctive complete form based on disjunctive operation is more suitable for enumeration in contrast with another form based on conjunctions. Conjunctive form is burdened with additional calculations, which are caused by logical negation. 2 Enumeration of Functions of Two Variables General aim of the proposed enumeration is to obtain a full collection of binary functions with two variables. In the present context only venjunctive functions are implied, that is functions containing at least one operation of venjunction.

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