SYNTHESIS OF THE FINITE STATE MACHINE WITH DATAPATH OF TRANSITIONS ACCORDING TO THE OPERATIONAL TABLE OF TRANSITIONS
Authors: Barkalov A. A. , Titarenko L. A. , Babakov R. M. 
Published: October 2022

Context. The problem of formalizing the description of a microprogram finite state machine based on the principle of operational transformation of state codes with the help of a modified transition table is considered. The object of research was a model of a microprogram finite state machine with datapath of transitions.
Objective. The goal of the work is development and research of a method for formally specifying a microprogram finite state machine with datapath of transitions in the form of a modified table of transitions containing sufficient information for synthesizing the logic circuit of the finite state machine in the basis of programmable logic devices.
Method. A new way of representing the formal solution of the problem of algebraic synthesis of a microprogram finite state machine with datapath of transitions in the form of an operational table of transitions is proposed. This table is a modification of the direct structural table traditionally used in the synthesis of microprogram finite state machines. The use of the previously known representation of the formal solution of the problem of algebraic synthesis in the form of a system of isomorphisms of automaton algebras is too formalized and makes it difficult to synthesize the logical circuit of the finite state machine due to the separate description of the transition and output functions. It is shown that the structure of a microprogram finite state machine with datapath of transitions requires information about the set of interpretations of state codes and the transition operations used to be entered into the traditional table of transitions. It is noted that the proposed operational table of transitions contains sufficient information for the synthesis of the logical circuit of the finite state machine. An example of constructing an operational table of transitions for a finite state machine given by a graph-scheme of the implemented control algorithm is shown. The example demonstrates various ways to interpret state codes. The procedure for synthesizing the circuit for generating codes of transition operations and the circuit for generating microoperations according to the operational table of transitions is proposed.
Results. An example of the implementation of the main stages of the synthesis of a finite state machine with datapath of transitions according to the operational table of transitions is considered. Examples of synthesized finite state machine models in the VHDL language are given, which take into account the peculiarities of the representation of finite state machine models in Xilinx Vivado CAD. The results of the synthesis of the finite state machine according to VHDL models in FPGA basis are shown.
Conclusions. The experiments carried out confirmed the sufficiency of the operational table of transitions for describing a microprogram finite state machine with operational transformation of state codes for the purpose of further synthesizing its logic circuit. Prospects for further research are the use of the proposed operational table of transitions in the development of various methods for the synthesis and optimization of microprogram finite state machine with operational transformation of state codes.