Volynskyy O. Methods of high-performance special processors constructing that are based on the theoretical and numerical basis of Krestenson

The object of research - the study of the processes of digital multy-category numbers of highly specialized processors in the basis of Rademacher-Krestenson; the subject of research - methods, ways and means of processing multy-category numbers and interbasis Rademacher-Krestenson conversion; novelty - we firstly developed an operation method of modular multiplication, in differentiated matrix-modular number system, which reduces the computational complexity of modular multiplications and exponentiations from 2 to 3 orders in comparison to the known systems; we also firstly developed a method for converting numbers from basis of Rademacher to basis of Krestenson using the recurrent scanning of binary numbers, starting with the senior level fo this allows to exclude the operation of comparison and subtraction for large binary numbers with pass-through transfer and to improve the performance of interbasis conversion of proportional category binary numbers; there was firstly developed a method of fast converting numbers from Rademacher positional basis system to Krestenson residual classes basis that by means of binary division multiplication and randomization of residues modulo codes keeps maximally separate the determination process of the final balance, the performance of which does not depend on the converted bit binary numbers category; the method of coding, modular addition and multiplication of numbers in the system of residual classes represented Running-positional codes Haar basis was further developed, which has replaced computing operations of adding and multiplication of binary numbers, matrix operations on modular codes balances the theoretical and numerical basis Krestenson and reduce the computational complexity of data arithmetic.