Conversion of numeration in modular arithmetic in the systems of residual classes with different bases

One of the stages of processing numbers in modular arithmetic, which requires the most amount of computer resources and thus significantly reduces the efficiency of the use of methods of modular arithmetic as the processing technology of numeric data in data processing equipment, is a step of converting the number of positional number system (PNS) in the modular (MS), and vice versa. However, in the processing of data it is sufficient to implement the MS-PNS conversion only at the start and at the very last stages of processing, and in the intermediate transformations to use conversion from one to another modular system. This article proposes a process for the conversion of numbers from one system to another residual classes without using Euclidean algorithm, as its multiple implementation is the most time-consuming step of finding representations of numbers in the SRC and the inverse transform notions of SRC in the required number. The procedure relies on the use of tables prepared beforehand. On the basis of this procedure, an algorithm that focuses directly on writing code can be developed. The assessment of the main characteristics of the conversion process is made. Quad-core processor, each core that can handle a 64-bit was considered as an example. The assessments presented in the paper showed that the cost of filling the tables were quite acceptable, which led to the conclusion about the possibility of the practical implementation of the developed procedure.