Influence of the number system in residual classes on the fault tolerance of the computer system

Abstract

The concept of increasing the fault tolerance of a computer system (CS) by using the existing natural redundancy, which depends on the number of systems used, is considered. The subject of this article is the methods and means of increasing the fault tolerance of CS and components based on the use of a non-positional number system in residual classes. It is shown that the use of the system of residual classes (SRC) as a number system ensures the fault-tolerant functioning of the real-time CS. This study considers a fault-tolerant CS operating in the SRC. The aim of this research is to show the influence of the non-positional number system in the SRC on the possibility of organizing the fault-tolerant functioning of a computer system. The object of this research is the process of fault-tolerant functioning of the CS in the SRC. This article provides an example of the operation of a fault-tolerant CS in the SRC given by a set of specific bases. The fault tolerance of CS in the SRC is ensured by the use of the basic qualities of the SRC by the method of active fault tolerance by using the procedure of gradual degradation. The level of fault tolerance of CS in the SRC in the example given in the article is achieved by reducing the accuracy of the calculations. This article considers two levels of degradation. Variants of algorithms for operating fault-tolerant CS in the SRC in the modes of replacement and gradual degradation are presented. Methods of system analysis, number theory, theory of computing processes and systems, and coding theory in the SRC were the basis of the conducted research. The results of the analysis of the specific example of the functioning of CS in the SRC given in the article, specified by four information and one control bases, showed the effectiveness of using non-positional code structures to ensure fault-tolerant operation. Conclusions. This article discusses the concept of increasing fault tolerance based on the use of the existing primary redundancy contained in the CS, due to the use of the basic properties of the non-positional number system in residual classes.