THE MAIN PROPERTIES OF THE NON-POSITIONAL NUMERICAL SYSTEM IN THE CLASS OF RESIDUES AND THEIR INFLUENCE ON THE STRUCTURE AND PRINCIPLES OF THE IMPLEMENTATION OF ARITHMETIC OPERATIONS OF THE COMPUTER SYSTEM
DOI:
https://doi.org/10.26906/SUNZ.2019.2.114Keywords:
computer system, non-positional numerical system, system of residual classes, speed of implementation of arithmetic operations, fault-tolerance, reliabilityAbstract
The subject of the study of the article is the methods in the processing of data in a computer system (CS), which functions in a non-positional numeral system in residual classes (SRC). The aim of the article is to study the influence of all the main properties of a non-positional numerical system on the structure of the CS and the principles of implementing arithmetic operations in the SRC. The following tasks are solved in the article. Formulation and study of the properties of the SRC, as well as obtaining the results of the influence of the properties of the SRC on the structure of the CS and the principles of realization of arithmetic operations of addition, subtraction and multiplication. Research methods: methods of analysis and synthesis of computer systems. The following results are obtained: the analysis of the results of the study of the properties of the SRC was summarized, as well as the result of the analysis of the influence of the properties of the SRC on the structure and implementation principles of arithmetic modular operations. Conclusions. The results of the study of the influence of the properties of the SRC on the structure of the CS and the principles of the implementation of arithmetic operations have shown that the use of the SRC leads to an increase in the speed of performing arithmetic operations and increases the fault tolerance of the functioning of the CS. In addition, the use of SRC allows you to make a unique system of monitoring, diagnostics and data error correction of the CS without stopping the calculations, which has no analogues in the positional numeral system (PNS). Improving the performance of the implementation of arithmetic operations in the SRC is achieved due to the possibility of organizing parallel data processing, as well as through the use of the tabular principle of the implementation of arithmetic operations. The use of the properties of the SRC determines the existence in the CS at the same time of three types of redundancy: structural, informational and functional. This, in turn, allows to increase the fault tolerance of non-positional computing structures in the SRC through the use of methods based on passive (permanent structural redundancy) and active (dynamic structural redundancy) fault tolerance.Downloads
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