Proof of the method of paired zeroing of numbers in a residue system

Abstract

The paper studies the problem of determining the lower boundary of number correction speed in computing systems operating in the basis of non-positional arithmetic in residual classes. The topicality of the problem is necessitated by the search of methods allowing reducing the time for digital processing of signals in non-positional neuroprocessors. The work considers the variants for error correction with single and multiple control bases of the residue system. The proof is provided that allows justifying the adequacy of the modified method that implements paired zeroing of numbers in the system of residual classes. It was shown that the suggested solutions allow considerably reducing the time expenses for digital processing of signals in neuroprocessors specialized in summation and multiplication operations. The proof is elaborated by the method of mathematical induction.