An important task of designing complex computer systems is to ensure high reliability. Many authors investigate this problem and solve it in various ways. Most known methods are based on the use of natural or artificially introduced redundancy. This redundancy can be used passively and/or actively with (or without) restructuring of the computer system. This article explores new technologies for improving fault tolerance through the use of natural and artificially introduced redundancy of the applied number system. We consider a non-positional number system in residual classes and use the following properties: independence, equality, and small capacity of residues that define a non-positional code structure. This allows you to: parallelize arithmetic calculations at the level of decomposition of the remainders of numbers; implement spatial spacing of data elements with the possibility of their subsequent asynchronous independent processing; perform tabular execution of arithmetic operations of the base set and polynomial functions with single-cycle sampling of the result of a modular operation. Using specific examples, we present the calculation and comparative analysis of the reliability of computer systems. The conducted studies have shown that the use of non-positional code structures in the system of residual classes provides high reliability. In addition, with an increase in the bit grid of computing devices, the efficiency of using the system of residual classes increases. Our studies show that in order to increase reliability, it is advisable to reserve small nodes and blocks of a complex system, since the failure rate of individual elements is always less than the failure rate of the entire computer system.