THE CONCEPT OF BUILDING HIGH-PERFORMANCE REAL-TIME SYSTEMS USING THE RESIDUE NUMBER SYSTEM

Abstract

The article examines the concept of building high-performance real-time information processing systems using the Residue Number System (RNS).The aim of the research is to improve the performance and fault tolerance of modern computing systems through the application of a non-positional number system, which enables parallel data processing, dynamic error correction, and adaptive regulation of accuracy and computational speed. The work emphasizes the key properties of RNS – independence of residues, equality of residues, and small digit length – and their impact on the performance and reliability of real-time systems.The research methodology is based on the principles of systems analysis, number theory, computational process theory, and systems modeling, as well as the simulation of modular arithmetic operations and error correction mechanisms. The study analyzes mathematical models of distributing informational and control residues to optimize the balance between speed, accuracy, and re- liability of computations. The implementation methods of modular arithmetic are considered, including adder-based, table-based, logical, and circular-shift principles, which improve processing speed and allow single-cycle execution of computations in real time.The scientific novelty of the work lies in the proposed methodology of dynamic redistribution of informational and con- trol residues in RNS to ensure high fault tolerance and adaptability of the system. The study proposes the use of control residues to maintain operability even in the case of multiple computational path failures, as well as the application of small-digit mod- ular arithmetic to enhance speed and reduce hardware complexity. It is shown that such a structure enables the simultaneous realization of three types of redundancy – structural, informational, and functional – which is critical for real-time systems.The conclusions of the study demonstrate that systems based on RNS provide significant acceleration of computationsthrough parallel execution on independent computational paths and operand decomposition, increase reliability due to error localization, and enable dynamic regulation of accuracy and computational speed. The implementation of such systems makes them effective for processing large data sets, digital signal and image processing, cryptography, neurocomputing, and stream- ing computation tasks, ensuring continuous operation even in the case of partial component failures.