THE CONSTRUCTION OF THE MODIFIED PERFECT FORM OF RESIDUAL CLASSES SYSTEM USING FACTORIZATION

M. M. Kasianchuk

Abstract


Context. The urgent task of finding modules of the system of residue classes, which characterize by increasing the speed of transition of numbers from the system of residue classes into decimal number system.

Objective is to develop a method of constructing modified fourth-module perfect form of the system of residue classes without procedure of finding of the absolute value for inverse element under number transition from residue number system to decimal number system.

Method. The method of determining a set of modules if modified perfect form of system’s of residue number was proposed which was based on factorization of numbers product. Usage of this form significantly reduced the computational complexity when arithmetic operations were performing on multi-digital numbers and transferring of numbers from the system of residual classes in the decimal system of calculation by eliminating of the searching procedure of the inverse element in absolute value and multiplying by the basic numbers. The conditions of discovering of any absolute number of modified perfect form of system of residual classes and two of them are unknown. An example of the proposed method for forth-module with modified perfect form system, which received all possible sets of modules with given smallest module. Tabular amounts are presented and analyzed according to the received image of modules.

Results. Utilization of the proposed method of modules selection which has constructed modified perfect form allows to increase the performance of computing systems operating in the system residual classes.

Conclusions. It’s the first time of discover of the method which allows to construct modified fourth-module perfect form of the system of residue classes based on factorization without complicated procedure of finding of the absolute value for inverse element. Present work helps to simplify the process of calculating digit number and transfer numbers from the system of residual classes into decimal system.


Keywords


System of residual classes; basic number; system of modules; modified perfect form; bit numbers; factorization.

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DOI: https://doi.org/10.15588/1607-3274-2017-3-6



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