1,721,473 research outputs found
Design of a residual adder in computer systems
No full textThe purpose of this article is to consider an algorithm for synthesizing the structure of the adder of two residuals ai and bi numbers A = (a1, a2,..., ai,..., ak ) and B = (b1, b2,..., bi,..., bk ) for an arbitrary value of the module mi of the residual class system (RCS), by organizing inter-bit connections between binary one-bit adders (BOA), the combination of which makes up the structure of modulo adder. The algorithm for the synthesis of adders by arbitrary modules is based on the usage of existing adders by module M = 2n -1, which consists of a set of sequentially located BOA, by introducing and using additional inter-bit connections of the form X↓i↑ j. Specific examples of the synthesis of structures of binary adders for various values of the RCS modules mi are given
Artificial Intelligence and Number System in Residual Classes
No full textThis article discusses 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 a non-positional number system in residual classes (RNS). When accepting the hypothesis about the holographic principle of information processing by the human brain, the expediency and effectiveness of building artificial intelligence systems based on the information processing model in the 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 concepts and 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 values of the RNS bases. So, the larger the number of RNS bases and the larger they are in value, the more accurately the information object G is described by means of frames. This fact confirms the expediency of using the RNS
Solving the Shortest Path Problem Using Integer Residual Arithmetic
No full textThe report considers solution to the problem of routing, the essence of which is to determine the shortest path length between any pair of computer network subscribers represented as an undirected graph, as one of the possible methods to increase the speed and performance of computer systems (CS). To carry out calculations and comparative analysis of the speed and productivity of CS in a positional binary number system (PNS) and in a non-positional number system in residual classes (residual number system-RNS), we consider one practical problem. Task is the routing problem, the essence of which is to determine the shortest path length, that is, to find the optimal data transmission route in the computer network
Mathematical Model of the Reliability of a Computer System which is Functioning in the Residual Class System, Taking into Account the Reliability of Switching Devices
No full textThe article discusses the option of constructing of the mathematical model of the reliability of a computer system (CS), which is functioning in the residual class system (RCS). In contrast to the known ones, the proposed mathematical model of reliability, in terms of the probability of failure-free operation, takes into account the influence of the reliability of switching devices on the process of functioning of the CS in the RCS. The results of studies of the proposed mathematical model of the reliability of the CS and the results of the comparative analysis of reliability showed that the use of the RCS provides higher reliability of the CS with lower hardware costs) than the majority tripleting method of the CS, which is widely used in the positional binary notation. This is achieved due to the fact that in the considered version of the mathematical model of the CS reliability, such types of redundancy as: structural, informational and functional, the presence of which is due to the properties of the RNS, are more fully taken into account. This circumstance makes it possible to apply the appropriate backup methods. The article shows that a gain in the amount of CS equipment is achieved from 2.5 to 42%
New technique for data hiding in cover images using adaptively generated pseudorandom sequences
No full textThe technology of direct spectrum spread is used in radio communication systems with multiple access. It is based on the use of pseudorandom (noise-like) discrete signals (sequences). In this paper steganography techniques based on spectrum spread are studied. Using noise-like signals, it is possible to hide information in cover images. We conduct experimental studies and show that the error rate in the restored informational messages is very high. This is due to the high correlation of discrete sequences and cover images. We offer a new technique when the statistical properties of cover images are taken into account when forming sequences. Our experiments show that the practical use of this approach can significantly reduce the error rate. The distortion of the image does not increase
Method of diagnostic of non-positional code structures in the system of residue classes basing on the usage of an alternative number set informativeness
No full textA method of diagnosis of data represented in the system of residue classes (SRC) is suggested in the article. It is shown, that the main disadvantage of existing methods of diagnosis data in SRC is a significant time of data diagnosis while the necessity of entering heavy informational redundancy to non-positional code structure (NCS) in SRC. The considered in the article method of diagnosis data in SRC allows increasing operability of a diagnosis procedure while entering minimal informational redundancy. The time of data diagnostic, compared to known methods, is decreasing firstly due to excluding the procedure of transforming numbers in SRC to positional notation as in known methods, i. e. eliminating a positional operation of numbers comparing. Secondly, the time of data diagnostic is decreased by reducing the quantity of SRC bases, which are giving the possibility of mistakes. Thirdly, the time of data diagnostic is decreased due to the usage of tabular sample value of an alternative set (AS) of numbers in SRC in one beat. The quantity of additionally entered informational redundancy is decrease by effective usage of inner informational redundancy existing in NCS. A specific example of the usage of the suggested method of diagnosis data in SRC is given. Therefore, the suggested method allows reducing the time of diagnosis of data errors in NCS, represented in SRC, which is increasing the diagnostic operability while entering minimal informational redundancy
The Procedure for Implementing the Operation of Multiplying Two Matrices Using the Residual Number System
No full textThe report considers solution to the problem of improving the speed implementation of the operation of multiplying two square matrices of the same dimension. To carry out calculations and comparative analysis of the speed of the multiplication operation, we consider a computer system (CS) in the positional binary number system (PNS) and in the non-positional number system in the residual classes (the residual number system - RNS). A comparative analysis of the performance of the CS was carried out with the same characteristics of the computing system: equal lengths of bit grids, the same command systems, the same methods of addressing operands and instructions, the same clock speed of the processor, the equal number of program commands, etc. When calculating the speed of the matrix multiplication operation, the fastest data processing method in RNS was used, based on the tabular principle
Noise immunity of the algebraic geometric codes
No full textLinear block noise-immune codes constructed according to algebraic curves (algebraic geometric codes) are considered, their design properties are evaluated, algorithms of construction and decoding are studied. The energy efficiency of the transmission of discrete messages by M-ary orthogonal signals in the application of algebraic geometric codes is studied; the achievable energy gain from the use of noise-immune coding is estimated. The article shows that in discrete channels without memory it is possible to obtain a significant energy gain, which increases with the transition to long algebraic geometric codes constructed from curves with a large number of points relative to the genus of the curve. It is found that the computational complexity of implementing algebraic geometric codes is comparable to other known noise-immune codes, for example, Reed-Solomon codes and others. Thus, high energy efficiency in combination with the acceptable computational complexity of implementation confirms the prospects of algebraic geometric codes use in modern telecommunication systems and networks to improve the noise immunity of data transmission channels
The Methods of Data Comparison in Residue Numeral System
No full textThe object of research is information processing in the systems of transmission and processing of digital data, which are built based on a non-positional number system in a residue number system (RNS). The purpose of the research is to develop a methods of data comparison, presented in RNS. To make this goal achieved, the existing methods of data comparison in RNS were analyzed and due to this a method of data comparison was developed, which allows performing the operation of number comparison in positive and negative numerical ranges. The following methods were used: the methods of analysis and synthesis, as well as the methods of numbers theory. It is recommended to use the presented algorithm, which is based on the developed method, in the practical implementation of the operation of comparing two numbers in RNS. The work presents the implementation of examples of the comparison operation based on the usage of the developed methods
Algorithms for determining residues modulo in a complex numerical domain
No full textAn important aspect of improving modern computer systems and their components is an increasing the speed of arithmetic calculations, including due to the use of new mathematical models and methods based on non-positional residue number systems. The increase in the volume of processed data in modern computer systems leads to the additional risks and threats of unintentional failures and denials of service. This is especially important when building fault-tolerant critical information systems in which failure or denial of service can lead to catastrophic consequences. The article discusses arithmetic operations in the ring of residue classes. These techniques make it possible to implement fast and fault-tolerant computing for modern computer systems and telecommunication networks. We propose an algorithm for calculating the residues of integer data in a complex numerical domain. The algorithm is based on the use of the first fundamental Gauss theorem, which establishes an isomorphism between complex and real residues. Examples of determining the residues of integer data in a complex numerical domain are presented, which clearly demonstrate the constructiveness of the proposed techniques
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