The coding of remainders number witch submitted the appropriate modules of residual classes system (RCS), made with data from complete system of the smallest non-negative residues (CSSNR) was showed in the article. In this aspect, CSSNR is the basis for the construction of non-positional code structure in RCS. Possible field of science and engineering, where there is an urgent need for fast, reliable and high-precision integer calculations were clarified and systematized in the paper. On the basis of studies of the properties of RCS were examined the advantages and disadvantages of using modular arithmetic (MA). Using the results of the analysis of problems of integer data and a set of positive attributes of MA, the classes of problems and algorithms, which using RCS, much more efficient binary positional numeral systems were defined in the article. Key words: residual classes system, modular arithmetic, positional numeral systems, complete system of the smallest non-negative residues, computer system and a data processing means witch represented in integer form, residual classes.
