DOI: https://doi.org/10.15588/1607-3274-2018-1-12

### GENERALIZING OF THE MATHEMATICAL MODEL OF MICROPROGRAM FINITE STATE MACHINE ON COUNTER

R. M. Babakov

#### Abstract

Context. The problem of developing of structural modifications of the microprogram finite state machine on the counter has been solved,
which can help reduce hardware expenses in the logical circuit of the microprogram finite state machine in comparison with the known
structures.
Objective. The goal of the work is to generalize the structural features of the microprogram finite state machine on the counter using a
mathematical model based on the intermediate algebra of transitions.
Method. The known mathematical model of a microprogram finite state machine on a counter, based on the representation of the
transition function in the form of two partial functions, is analyzed. The use of an incremental counter in the structure of the finite state machine is expressed in this model by an intermediate algebra of transitions whose signature is formed by a single incremental function. In this case, the argument of the function is the code of the current state of the finite state machine, interpreted as an unsigned integer. For the considered mathematical model, a number of generalizations are made regarding the number of intermediate algebras of transitions, their signatures and carriers. Changes in the mathematical model and the structure of the finite-state machine on the counter, which are a
consequence of the generalizations made, are analyzed.
Results. On the basis of the generalizations made, a generalized structural scheme and a mathematical model of a microprogram finitestate machine with a noncanonical way of realizing the transition function are obtained. Experimental research of the effectiveness of the
developed generalized structure of MPA on the criterion of hardware costs has been carried out.
Conclusions. The results obtained in this paper can be used in the development of new structures and formal methods for the synthesis
of microprogram finite state machines with noncanonical realization of the transition function, oriented to optimizing the hardware expenses
in the logical circuit of the automaton.

#### Keywords

microprogram finite state machine on counter; mathematical model; intermediate algebra of transitions; hardware expenses

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Copyright (c) 2018 R. M. Babakov