Kunitskaya S. The method and means of the synthesis of fast arithmetic units on the basis of positional notations.

The object of research is the synthesis of discrete systems based on the information redundancy of positional number systems. The aim of the thesis is to develop the method of constructing arithmetic units based on the synthesis of positional number systems, which will provide an increase in operation the speed due to the introduction and the usege of information as well the hardware redundancy. In developing jf the integrated approach to the study of redundant binary positional number systems: the theory of redundancy the teoryg information, the theory of Error Control codes were used. For the synthesis and the study of number systems with the introduction of information redundancy: basics of discrete mathematics, the set theory, mathematical modeling methods and the theory of recurrent sequences were used; in the modeling and functional circuits using discrete devices: boolean algebra, the theory of reliability, the development of a method of construction of arithmetic units - system analysis, diskret mathematics, algorithms and simulation methods of arithmetic units were used. In the process of solving the problems, the author obtained the following results: 1) for the time i the model of positional number system based on weighting grades and code numbers, by limiting the number of digits, while maintaining its properties, provided a comprehensive study of the automation of redundant binary positional number systems is proposed and 2) the methods of the synthesis and analysis of arithmetic units based on the introduction of information redundancy by calculating the characteristics of the number system on the positional number system model, which are allowed for the number system, which will provide increased performance while reducing the complexity of the hardware have got futher development implementation, and 3) the method of the arithmetic constructing units is firstly developed through the introduction of information redundancy and the calculation of the characteristics of the number system for their models that enable to get the number system and to synthesize on the basis of their summers with great speed, and 4) the model of discrete devices by implementing the method of arithmetic units of construction, which provided the improvement performance in adders reducing hardware complexity futher developed. The results of the work are implemented on enterprises and in organizations of the Ministry of Industrial Policy, the Ministry Science and Education, Youth and Sport.