Features of machine arithmetics of high-performance modular computing structures

The procedures for generating a modular code for various variants of modular number systems are herein considered. The features of machine arithmetic of the basic integral characteristics of the modular code are noted. Proof of the theorem on minimally redundant modular coding is proposed as an effective way to reduce the time of computing the integral characteristics of a modular code. It is shown that the introduction of minimal redundancy into a modular code greatly simplifies the calculation of interval-index characteristics and related forms of representing integers when implementing a number of non-modular operations. We noted a certain decrease in the efficiency of minimally redundant modular number systems if the number of integral characteristics of the modular code, the sign of the number or digits of the polyadic code increases in the used applications. This circumstance does not reduce the expediency of using minimally redundant modular number systems in a wide range of applications of minimally redundant modular arithmetics, including digital signal processing, information security, information technology, etc.