The report considers correction codes with mutually non-prime bases (CMNPB). To date, almost no one has been engaged in a deep study of the corrective properties of systems of residual classes (SRC), the bases of which are not mutually prime numbers. Such a system has certain corrective properties, which makes it necessary to assess the possibility and feasibility of using CMNPB to increase the reliability of computing in computer systems (CS). For the purpose of further research and development of CMNPB, we will consider a number of scientific statements, the use of the results of which will allow us to more fully study the corrective properties of codes with non-prime bases. Algorithms for monitoring and correcting errors in the SRC with mutually non-prime in pairs bases have been developed. Using these algorithms makes it relatively easy to implement a procedure for detecting and correcting one-time errors. Note that by the simplicity of the design of the decoder circuits, CMNPB have no analogues in the positional number systems. This is achieved by limiting the class of possible correctable errors, by introducing additional hardware redundancy in the representation of code words.

This paper proposes an improved method for diagnosing errors of computer devices, which process economic data in computer systems, by increasing efficiency. The object of research is the processes of control and diagnosis of data errors, in the class of residuals (CR). The improved method of diagnosing economic data represented in the non-positional system of calculation in CR is based on the application of orthogonal bases of partial sets of bases. The use of these bases makes it possible to organize the process of parallel processing of the projections of the output number of the non-positional code structure. This makes it possible to increase the efficiency of data diagnostics by n times, depending on the length of the bit grid of computer systems. For a single-byte computer system, the efficiency of data diagnosis increases by 1.2 times compared to the existing method based on the zeroing principle. At the same time, the effectiveness of operational control and diagnostics systems for data processing in CR with the growth of bit grids has been proven. Based on the results, it is shown that, unlike the correction codes used in the positional counting system, the arithmetic codes in CR have additional correction capabilities. An example of a specific implementation of the process of applying operational control and diagnosing errors in the processing of economic data presented in CR is given. The improved diagnostic method will make it possible (in comparison with existing diagnostic methods) to reduce the time, which increases the efficiency of the diagnostic procedure of data operating in CR. The results give grounds for asserting that, based on the improved method and the developed algorithm for the implementation of data diagnostics, it is possible to synthesize a device for reliable and operational control and diagnostics of economic data operating in CR