Synthesis Of Computer Systems Research Articles

THE STRUCTURE OF THE COMPUTER SYSTEM IN THE RESIDUAL CLASSES

The subject of the article is the formulation and solution of the inverse problem of optimal redundancy in the system of residual classes (RNS) based on the use of the dynamic programming method. The solution of this problem makes it possible to improve the reliability of the operation of computer systems and components (CSC) in the RNS. The purpose of the article is to increase the reliability of the functioning of CSC, which are built on the basis of the use of RNS, without reducing the speed of calculations, as well as to calculate and compare the reliability, in terms of the probability of failure-free operation, of CSC in RNS and a tripled computing system that operates in a positional binary number system (PNS). Tasks: to analyze the influence of the number system used on the reliability of the CSC, taking into account the primary and secondary redundancy; to synthesize a computing system in RNS for a l-byte bit grid based on the use of the passive fault tolerance method (constant structural redundancy); formulate and solve the inverse problem of optimal redundancy in RNS based on the use of the dynamic programming method; to check the correctness of the results obtained, calculate the conditional amount of computer system equipment in the residual classes; evaluate the efficiency of using RNS to improve reliability when building a redundant CSC in relation to a redundant CSC in the PNS. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS, reliability theory. The following results are obtained. The paper shows that the use of PNS as a number system does not allow a radical increase in the performance and reliability of CSC. In this regard, the article developed the concept of using RNS as a number system for constructing a CSC. Based on this, the inverse problem of optimal redundancy in RNS is formulated and solved. Conclusions. As shown by the results of calculations and comparative analysis, the use of RNS provides a higher reliability of the CSC than the majority three-channel computing system in the PNS. The obtained research results can be used for the synthesis of fault-tolerant computer structures in RNS.

MATHEMATICAL MODEL OF COMPUTER SYSTEM RELIABILITY IN RESIDUAL CLASSES

The subject of the article is the construction of a mathematical model of the reliability of a computer system (CS) that operates in a system of residual classes (RNS). This mathematical model is based on the use of structural sliding reservation. The purpose of the article is to increase the reliability of the CS, which operates in the system of residual classes, as well as to calculate and compare the reliability, in terms of the probability of failure-free operation, of the CS in the RNS and the ternary computing system, which operates in the positional binary number system (PBNS). Tasks: to analyze the influence of the number system used on the reliability of the CS; to investigate the properties of the RNS and determine their influence on the structure of the CS in the RNS; build a mathematical model of reliability and, on its basis, perform the calculation and comparative analysis of the reliability of the CS in the RNS and the tripled CS in the PBNS. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS, reliability theory. The following results are obtained. The paper shows that the provision of a given level of reliability in the design of the CS using the RNS is due to the presence of various types of redundancy at the same time: structural, informational, temporal, functional and load. In RNS, these types of redundancy can be effectively used to improve the reliability of the CS. The CS in the RNS represents a computational structure that is identical in structure and principle of operation to the sliding structural redundancy model in the PBNS in the case of a loaded (hot) mode of operation of the redundant elements. Proceeding from this, the paper presents a mathematical model of the reliability of the CS in the RNS. In this paper, the calculation and comparative analysis of the reliability of a tripled computing structure in a PBNS with an ideal majority element and a CS in an RNS with an ideal reliability automaton are carried out. Conclusions. As shown by the results of calculations and comparative analysis in some time intervals of operation, the probability of non-failure operation of the CS in the RNS is higher than the probability of non-failure operation of the aircraft in the PBNS with a tripled majority structure. This implies the effective use of the RNS to improve the reliability of the CS.

THE CONCEPT OF PERFORMING THE ADDITION OPERATION IN THE SYSTEM OF RESIDUAL CLASSES

The subject of the article is the development of a method for implementing the arithmetic operation of adding the residuals of numbers, which are represented in the system of residual classes (RNS). This method is based on the use of positional binary adders. The purpose of the article is to improve the performance of computer systems (CS) and their components by introducing new ways of organizing calculations based on the use of RNS. Tasks: to analyze and identify the shortcomings of the existing number systems that are used in the construction of computer systems and components; explore possible ways to eliminate the identified deficiencies; explore the structure of binary positional adders, taking into account the scheme for adding two residues of numbers modulo RNS; to develop a method for constructing adders modulo RNS, which is based on the use of a set of binary single-digit positional adders. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS. The following results are obtained. The paper shows that one of the promising ways to improve the performance of the CS is the use of RNS. The mathematical basis of RNS is the Chinese remainder theorem, which states that an integer operation on one large modulus can be replaced by a set of operations on coprime small modules. This opens up broad prospects for optimizing calculations. On the one hand, it is possible to significantly simplify the performance of complex and cumbersome calculations, including on low-resource computing platforms. On the other hand, calculations for different modules can be performed in parallel, which increases the performance of the CS. Conclusions. The article considers the operation of adding two numbers. This operation is the basis for both traditional positional number systems and RNS, i.e. forms the computational basis of all existing CS components. A new method for calculating the sum of the residuals of numbers modulo an arbitrary is proposed, and examples are given that clearly demonstrate the effectiveness of the proposed method. This method can be used in various computer applications, including for improving computing performance, ensuring fault tolerance, etc.

THE CONCEPT OF USING THE NUMBER SYSTEM IN THE RESIDUAL CLASSES FOR BUILDING ARTIFICIAL INTELLIGENCE SYSTEM

The subject of the article is the consideration of the concept of constructing an artificial intelligence (AI) system based on the use of a non-positional system of residual classes (RNS). This concept is based on the hypothesis of the holographic principle of building the memory of biological systems. The purpose of the article is to consider a method for constructing an information model of the process of information processing by the human brain, based on the ass umption that the storage and processing of information is carried out in the RNS. Tasks: to consider a model of the process of information processing by the human brain; consider the proposed model of information processing by the human brain in the RNS; to study the influence of RNS properties in the creation of intelligent computing systems. Research methods:methods of analysis and synthesis of computer systems, data analysis, number theory, coding theory in RNS. The following results are obtained. The article considers a model of the process of information processing by the human brain, based on the assumption that the storage and processing of information is carried out in the RNS. When accepting the hypothesis of the holographic principle of information processing by the human brain, the expediency and efficiency of building AI systems based on the information processing model in RNS is obvious. This is due to the fact that the principles and methods of information processing in the RNS are in good agreement with modern ideas about the process of information processing by the human brain. The accuracy of the description (representation) of the information object G depends on the number and value of RNS bases. So, the greater the number of RNS bases and the greater their value, the more accurately the information object G is described using frames. This fact confirms the feasibility of using RNS. Conclusions. The main idea of the study is to consider the hypothesis of the holographic principle of building the memory of biological systems. In this case, the failure of one or more memory cells does not affect the normal functioning of the biological model of the brain, i.e. each unit of initial information is distributed over the entire surface of the hologram. In the article, AI is presented as a model of computational processes operating in RNS. Thus, the expediency and efficiency of building AI systems based on the information processing model functioning in the RNS is assessed as obvious.

METHOD FOR DIAGNOSING DATA ERRORS OF A COMPUTER SYSTEM FUNCTIONING IN THE SYSTEM OF RESIDUAL CLASSES

The subject of the article is the development of a method for diagnosing data errors of a computer system functioning in the residue number system (RNS). This method is based on the tabular principle of data diagnostics operation implementation. The purpose of the article is to reduce the time of performing the operation of diagnosing the data of a computer system that functions in the RNS in the dynamics of the computational process. Tasks: to analyze the possible application of RNS as a number system in computer data processing systems; to investigate existing methods of data diagnostics and identify possible shortcomings in data diagnostics in the dynamics of the computational process with the introduction of minimal information redundancy; to develop a method for diagnosing the data presented in the RNS, which is based on the tabular principle of the implementation of the diagnostic operation. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS. The following results were obtained. The work shows that the data diagnostics is carried out after the control operation has been performed. To carry out the operation of diagnosing data in the RNS, when one-time errors occur, methods for determining an alternative set (AS) of numbers are used. In this case, the main disadvantage of the considered methods is the considerable time required to determine the AS. To reduce the time for determining the AC numbers in the work, the method for diagnosing data in the RNS has been improved. Improvement of the method involves the compilation of a table (the first stage) of correspondence to each correct number of a possible set of incorrect numbers when one-time errors occur in the data. Based on the analysis of the contents of the table of the first stage, a table (of the second stage) is drawn up of the correspondence of each incorrect number to the possible values of the correct numbers. Conclusions. The use of the improved method increases the efficiency of diagnostics of the data presented in the RNS by reducing the time for determining the AC numbers. This is achieved by quickly fetching pre-calculated AC table values.

THE DATA DIAGNOSTIC METHOD OF IN THE SYSTEM OF RESIDUE CLASSES

The subject of the article is the development of a method for diagnosing data that are presented in the system of residual classes (SRC). The purpose of the article is to develop a method for fast diagnostics of data in the SRC when entering the minimum information redundancy. Tasks: to analyze and identify possible shortcomings of existing methods for diagnosing data in the SRC, to explore possible ways to eliminate the identified shortcomings, to develop a method for prompt diagnosis of data in SRC. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in SRC. The following results were obtained. It is shown that the main disadvantage of the existing methods is the significant time of data diagnostics when it is necessary to introduce significant information redundancy into the non-positional code structure (NCS). The method considered in the article makes it possible to increase the efficiency of the diagnostic procedure when introducing minimal information redundancy into the NCS. The data diagnostics time, in comparison with the known methods, is reduced primarily due to the elimination of the procedure for converting numbers from the NCS to the positional code, as well as the elimination of the positional operation of comparing numbers. Secondly, the data diagnostics time is reduced by reducing the number of SRC bases in which errors can occur. Third, the data diagnostics time is reduced due to the presentation of the set of values of the alternative set of numbers in a tabular form and the possibility of sampling them in one machine cycle. The amount of additionally introduced information redundancy is reduced due to the effective use of the internal information redundancy that exists in the SRC. An example of using the proposed method for diagnosing data in SRC is given. Conclusions. Thus, the proposed method makes it possible to reduce the time for diagnosing data errors that are presented in the SRC, which increases the efficiency of diagnostics with the introduction of minimal information redundancy.

SYNTHESIS OF STRUCTURE OF THE ADDER BY MODULE

The subject of the article is the study of the structure of low-bit binary adders for an arbitrary modulus of the residual class system (RCS). The purpose of this article is to develop an algorithm for synthesizing the structure of the adder of two residuals of numbers by an arbitrary value of the RCS module, by organizing inter-bit connections between the binary digits of the adder, the combination of which determines the structure of the adder modulo. Tasks: to investigate the possibility of performing the operation of addition of two residuals in RCS based on positional binary adders; to analyze the influence of additionally introduced interdigit connections into the positional binary adder on the value of the contents of this adder; to develop an algorithm for the synthesis of an adder by an arbitrary RCS module. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RCS. The following results were obtained. It is shown in the work that the introduction of additional interdigit connections in a positional binary adder allows changing the contents of this adder. The rules for the introduction of these additional links are formulated, on the basis of which an algorithm for the synthesis of an adder by an arbitrary RCS modulus is obtained. Specific examples of the synthesis of structures of binary adders for various values of the RCS modules are given. Conclusions. Thus, the paper proposes an algorithm for the synthesis of an adder by an arbitrary RCS module, which is based on the use of positional binary adders, by introducing additional inter-bit connections. The application of the considered algorithm expands the functionality of positional binary adders

IMPLEMENTATION OF THE ARITHMETIC ADDITION OPERATION IN THE SYSTEM OF RESIDUAL CLASSES

Предметом статті є розробка методу реалізації арифметичної операції додавання чисел, які представлені у системі залишкових класів (СЗК). Даний метод ґрунтується на основі використання принципу кільцевого зсуву (ПКЗ). Метою статті є зменшення часу реалізації арифметичної операції додавання чисел, які представлені у СЗК. Задачі : провести аналіз і виявити недоліки існуючих систем числення, які використовуються при побудові комп'ютерних систем і компонентів, дослідити можливі шляхи усунення виявлених недоліків, зробити оцінку часу реалізації арифметичної операції додавання на основі використання розробленого методу. Методи дослідження : методи аналізу та синтезу комп'ютерних систем, теорія чисел, теорія кодування у СЗК. Отримано наступні результати . Показано, що основним принципом реалізації арифметичних операцій у позиційних системах числення, є використання двійкових суматорів. При цьому використання таких систем числення обумовлює наявність міжрозрядних зв'язків, що в свою чергу збільшує час реалізації арифметичних операцій, а також зумовлює виникнення помилок. Встановлено, що використання непозиційної системи числення у залишкових класах дозволяє усунути зазначені недоліки, за рахунок використання основних властивостей СЗК. Особливість розробленого методу полягає у тому, що результат операції додавання чисел може бути знайдений послідовними циклічними зсувами бітів вмісту блоків даних по відповідним модулям СЗК. Використання ПКЗ дозволяє виключити вплив межрозрядних зв'язків між залишками чисел, що оброблюються, це дозволяє зменшити час реалізації операції додавання двох чисел у СЗК. Висновки . Результати проведених досліджень показали, що використання СЗК дозволяє усунути існуючі недоліки позиційних систем числення, а також підвищує швидкодію реалізації арифметичних операцій.

CONTROL AND CORRECTION OF DATA ERRORS IN A RESIDUE CLASS

The subject of the research in the article is the methods of control and correction of single errors of integer data are presented in the residue class (RC), which allows to increase the efficiency of using RC when building computer systems and components. The purpose of the article is to develop a method for correcting single data errors in RC. Tasks: to study the code structures presented in RC to determine the possibility of control and correction of data errors; to investigate the effect of RC properties on data control and correction operations; to develop a method for correcting single data errors in RC. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RC. The following results are obtained. An analysis of the correcting capabilities of codes in RC showed the high efficiency of using non-positional code structures, which is due to the presence of primary and secondary redundancy in such structures. The article presents a method for correcting one-time data errors in RC. Examples of detecting and correcting data errors in RC code are given, which confirms the theoretical results obtained. Conclusions. Studies have shown that the use of codes in RC makes it possible to build an effective system for monitoring and correcting data errors with the introduction of minimal code redundancy. That is, when certain conditions are met, the introduction of one control base allows not only monitoring, but also correction of single data errors

COHERENT CONCURRENT TASKS SCHEDULING AND RESOURCES ASSIGNMENT IN DEPENDABLE COMPUTER SYSTEMS DESIGN

The paper includes a proposal of a new model of coherent concurrent tasks scheduling and a of resources assignment, that are characteristic for the problem of dependable system synthesis. Optimal tasks scheduling, partition at resources, allocation tasks and resources are basic problems in high-level synthesis of computer systems. Coherent synthesis may have a practical application in developing tools for computer aided rapid prototyping of such systems.

Review of 'Analysis and Synthesis of Computer Systems' (Gelenbe, E., and Mitrani, I.; 1980)

Review of 'Analysis and Synthesis of Computer Systems' (Gelenbe, E., and Mitrani, I.; 1980)