Operational formation of state codes in microprogram automata
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OPERATIONAL FORMATION OF STATE CODES IN MICROPROGRAM AUTOMATA A. A. Barkalova and R. M. Babakov b
UDC 681.324
Abstract. A new principle is proposed for the realization of transition functions in a microprogram automaton. The principle is based on the representation of the code of an automaton state in the form of an arithmetic value transformed by arithmetic-logical operations. A structure of a microprogram automaton with operational formation of transitions is proposed. Keywords: microprogram automaton, flowgraph of an algorithm, state, transition operation, optimization of hardware expenditures. INTRODUCTION A control unit (CU) is one of central units of modern digital computing systems, which determines key features of such a system in many respects [1–3]. Among traditional methods of construction of CUs, we single out their representation in the form of finite Mealy or Moore automata with their subsequent realization in the form of a control automaton (CA) with “rigid” logic (which is also called a microprogram automaton (MPA)) according to the principle of microprogram control [2]. The problem of designing CUs permanently arises in developing digital systems since, for various systems, it is precisely a CU that should be designed for each system from the very outset. Since a CU is specified by its operation algorithm that can be implemented in the form of various finite automata, the problem of synthesis of a CU is reduced to the choice of a structure providing the satisfaction of optimization criteria as applied to the element basis being used. The complexity of problems solved by computing systems permanently increases, which implies the topicality of the problem of developing new efficient CU structures in which cost characteristics of CU circuits are optimized. The objective of this work is the development of a new MPA structure that is based on a special principle of realization of microprogram transitions and allows one to decrease hardware expenditures for a CU circuit. CANONICAL METHOD OF SYNTHESIS OF MPAs This method is based on the structural completeness theorem proved by V. M. Glushkov [1]. A result of application of this method is a system of equations specifying the dependence of output signals and signals applied to inputs of memory elements on external signals arrived at the inputs of an automaton and signals arrived from outputs of these memory elements. These equations are called canonical. It should be noted that the traditional form of representation of canonical equations of structural automata are Boolean functions (BFs) combining Boolean variables with the help of logical operations. In this case, an abstract statement of the synthesis problem for an automaton is based on the following two criteria: (1) a minimal number of states in the automaton; (2) finding of a minimal disjunctive forms (DNFs) of transition and output functions. a
University of Zielona GËra, Zielona GËra, Poland, [email protected]. bState University of Informatics and Artificial Intelligence, Donetsk, Ukra
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