ON THE TRANSFORMATION OF REPRESENTATION OF NUMBERS IN THE RESIDUO FROM ONE MODULE SYSTEM TO ANOTHER

Yu. D. Polissky

Abstract


Purpose. The purpose of this work is the theoretical foundation of one of the approaches to improve the effectiveness of the number system in nonpositional residual classes non-modular, so-called complex operation, the realization of which requires knowledge of all the digits of operands charges. The operation consists in transformation of the representation of one of the modules of its representation in the other system of modules. Methodology. The tools of research methodology are the system analysis, theory of numbers, the Chinese remainder theorem. The technique uses a representation of number as its residues, and in the polyadic code and is based on the determination of the balance of the module based on the obtained residues on the remaining modules of the original system. Such a determination is performed by sequentially subtracting of constants from the obtained residues of the original number and summing of these constants to the results, which are formed by the required modules. Thus, constant at each iteration are selected from pre-calculated tables depending on the value of the residue in the analyzed discharge. The proposed method is algorithmically simple and at circuit implementation can create the computational structures of high performance and reliability. Findings. The theoretical justification for this approach to obtain effective solutions of non-modular transformation operation in the system of residual classes for transition from representation of the number by the one system of units to its representation by the other system of modules. Originality. A theoretical justification of the proposed approach to the solution of a non-modular conversion operations in the residue number system for the transition from representation of number in one system of units to its representation in the other system of modules was proposed. This approach is appropriate to consider as one of the areas of research ways to improve the computational efficiency. Practical value. It follows from the importance of the theoretical conclusions and results of the study. It consists in the fact that it is justified a simple and effective approach to the problem of implementation of non-modular conversion operations in the residue number system for the transition from representation of the number in one system of units to its representation in the other system of modules. The above mentioned solutions have a high speed and may be effective in the development of modular computing structures for advanced information technologies.


Keywords


residual classes; number; complex operations; positional characteristic; system of modules; iteration

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DOI: https://doi.org/10.15802/stp2016/74735

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