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Relevant bibliographies by topics / Number system for modular arithmetic

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Academic literature on the topic 'Number system for modular arithmetic'

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Published: 25 May 2024

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Journal articles on the topic "Number system for modular arithmetic"

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Khani, Elham. "Efficient Montgomery Modular Multiplication by using Residue Number System." INTERNATIONAL JOURNAL OF MANAGEMENT & INFORMATION TECHNOLOGY 2, no. 1 (2012): 56–62. http://dx.doi.org/10.24297/ijmit.v2i1.1410.

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Residue number system is a carry free system that performs arithmetic operation on residues instead of the weighted binary number. By applying Residue Number System (RNS) to Montgomery modular multiplication the delay of modular multiplication will be decreased. Modular multiplication over large number is frequently used in some application such as Elliptic Curve Cryptography, digital signal processing, and etc.By choosing appropriate RNS moduli sets the time consuming operation of multiplication can be replaced by smaller operations. In addition because of the property of RNS, arithmetic oper

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Guzhov, Vladimir I., Ilya O. Marchenko, Ekaterina E. Trubilina, and Dmitry S. Khaidukov. "Comparison of numbers and analysis of overflow in modular arithmetic." Analysis and data processing systems, no. 3 (September 30, 2021): 75–86. http://dx.doi.org/10.17212/2782-2001-2021-3-75-86.

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The method of modular arithmetic consists in operating not with a number, but with its remainders after division by some integers. In the modular number system or the number system in the residual classes, a multi-bit integer in the positional number system is represented as a sequence of several positional numbers. These numbers are the remainders (residues) of dividing the original number into some modules that are mutually prime integers. The advantage of the modular representation is that it is very simple to perform addition, subtraction and multiplication operations. In parallel executio

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Krasnobayev, V. A., A. S. Yanko, and D. M. Kovalchuk. "METHODS FOR TABULAR IMPLEMENTATION OF ARITHMETIC OPERATIONS OF THE RESIDUES OF TWO NUMBERS REPRESENTED IN THE SYSTEM OF RESIDUAL CLASSES." Radio Electronics, Computer Science, Control, no. 4 (December 3, 2022): 18. http://dx.doi.org/10.15588/1607-3274-2022-4-2.

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Context. Implementation of modular arithmetic operations of addition, subtraction and multiplication by a tabular method based on the use of the tabular multiplication code. The object of the study is the process of tabular implementation of basic arithmetic operations on the residues of numbers represented in the system of residual classes. Objective. The goal of the work is to develop methods for the tabular implementation of the arithmetic operations of multiplication, addition and subtraction of the residues of two numbers based on the use of the tabular multiplication code. Me

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Shevelev, S. S. "RECONFIGURABLE COMPUTING MODULAR SYSTEM." Radio Electronics, Computer Science, Control 1, no. 1 (2021): 194–207. http://dx.doi.org/10.15588/1607-3274-2021-1-19.

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Context. Modern general purpose computers are capable of implementing any algorithm, but when solving certain problems in terms of processing speed they cannot compete with specialized computing modules. Specialized devices have high performance, effectively solve the problems of processing arrays, artificial intelligence tasks, and are used as control devices. The use of specialized microprocessor modules that implement the processing of character strings, logical and numerical values, represented as integers and real numbers, makes it possible to increase the speed of performing arithmetic o

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Schevelev, S. S. "Reconfigurable Modular Computing System." Proceedings of the Southwest State University 23, no. 2 (2019): 137–52. http://dx.doi.org/10.21869/2223-1560-2019-23-2-137-152.

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Purpose of research. A reconfigurable computer system consists of a computing system and special-purpose computers that are used to solve the tasks of vector and matrix algebra, pattern recognition. There are distinctions between matrix and associative systems, neural networks. Matrix computing systems comprise a set of processor units connected through a switching device with multi-module memory. They are designed to solve vector, matrix and data array problems. Associative systems contain a large number of operating devices that can simultaneously process multiple data streams. Neural networ

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Selianinau, Mikhail, and Yuriy Povstenko. "An Efficient CRT-Base Power-of-Two Scaling in Minimally Redundant Residue Number System." Entropy 24, no. 12 (2022): 1824. http://dx.doi.org/10.3390/e24121824.

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In this paper, we consider one of the key problems in modular arithmetic. It is known that scaling in the residue number system (RNS) is a rather complicated non-modular procedure, which requires expensive and complex operations at each iteration. Hence, it is time consuming and needs too much hardware for implementation. We propose a novel approach to power-of-two scaling based on the Chinese Remainder Theorem (CRT) and rank form of the number representation in RNS. By using minimal redundancy of residue code, we optimize and speed up the rank calculation and parity determination of divisible

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Chernov, V. M. "Number systems in modular rings and their applications to "error-free" computations." Computer Optics 43, no. 5 (2019): 901–11. http://dx.doi.org/10.18287/2412-6179-2019-43-5-901-911.

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The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of d

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Kalmykov, Igor Anatolyevich, Vladimir Petrovich Pashintsev, Kamil Talyatovich Tyncherov, Aleksandr Anatolyevich Olenev, and Nikita Konstantinovich Chistousov. "Error-Correction Coding Using Polynomial Residue Number System." Applied Sciences 12, no. 7 (2022): 3365. http://dx.doi.org/10.3390/app12073365.

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There has been a tendency to use the theory of finite Galois fields, or GF(2n), in cryptographic ciphers (AES, Kuznyechik) and digital signal processing (DSP) systems. It is advisable to use modular codes of the polynomial residue number system (PRNS). Modular codes of PRNS are arithmetic codes in which addition, subtraction and multiplication operations are performed in parallel on the bases of the code, which are irreducible polynomials. In this case, the operands are small-bit residues. However, the independence of calculations on the bases of the code and the lack of data exchange between

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Rahn, Alexander, Eldar Sultanow, Max Henkel, Sourangshu Ghosh, and Idriss J. Aberkane. "An Algorithm for Linearizing the Collatz Convergence." Mathematics 9, no. 16 (2021): 1898. http://dx.doi.org/10.3390/math9161898.

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The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers for which the inflation propensity remains so unpredictable it could be used to generate reliable proof-of-work algorithms for the cryptocurrency industry; it has so far resisted every attempt at linearizing its behavior. Here, we establish an ad hoc equivalent of modular arithmetics for Collatz sequences based on five arithmetic rules that we prove apply to the entire Collatz dynamical system and for which the iterations exactly define the full basin of attractions leading to any odd number. We further

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Chervyakov, Nikolay, Pavel Lyakhov, Mikhail Babenko, et al. "A Division Algorithm in a Redundant Residue Number System Using Fractions." Applied Sciences 10, no. 2 (2020): 695. http://dx.doi.org/10.3390/app10020695.

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The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based

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Dissertations / Theses on the topic "Number system for modular arithmetic"

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Néto, João Carlos. "Método de multiplicação de baixa potência para criptosistema de chave-pública." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/3/3141/tde-23052014-010449/.

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Esta tese estuda a utilização da aritmética computacional para criptografia de chave pública (PKC Public-Key Cryptography) e investiga alternativas ao nível da arquitetura de sistema criptográfico em hardware que podem conduzir a uma redução no consumo de energia, considerando o baixo consumo de potência e o alto desempenho em dispositivos portáteis com energia limitada. A maioria desses dispositivos é alimentada por bateria. Embora o desempenho e a área de circuitos consistem desafios para o projetista de hardware, baixo consumo de energia se tornou uma preocupação em projetos de sistema crí

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Dosso, Fangan Yssouf. "Contribution de l'arithmétique des ordinateurs aux implémentations résistantes aux attaques par canaux auxiliaires." Electronic Thesis or Diss., Toulon, 2020. http://www.theses.fr/2020TOUL0007.

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Cette thèse porte sur deux éléments actuellement incontournables de la cryptographie à clé publique, qui sont l’arithmétique modulaire avec de grands entiers et la multiplication scalaire sur les courbes elliptiques (ECSM). Pour le premier, nous nous intéressons au système de représentation modulaire adapté (AMNS), qui fut introduit par Bajard et al. en 2004. C’est un système de représentation de restes modulaires dans lequel les éléments sont des polynômes. Nous montrons d’une part que ce système permet d’effectuer l’arithmétique modulaire de façon efficace et d’autre part comment l’utiliser

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Marrez, Jérémy. "Représentations adaptées à l'arithmétique modulaire et à la résolution de systèmes flous." Electronic Thesis or Diss., Sorbonne université, 2019. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2019SORUS635.pdf.

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Les calculs modulaires entrant en jeu dans les applications en cryptographie asymétrique utilisent le plus souvent un modulo premier standardisé, dont le choix n’est pas toujours libre en pratique. L’amélioration des opérations modulaires est centrale pour l’efficacité et la sécurité de ces primitives. Cette thèse propose de fournir une arithmétique modulaire efficace pour le plus grand nombre de premiers possible, tout en la prémunissant contre certains types d’attaques. Pour ce faire, nous nous intéressons au système PMNS utilisé pour l’arithmétique modulaire, et proposons des méthodes afin

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Vonk, Jan Bert. "The Atkin operator on spaces of overconvergent modular forms and arithmetic applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:081e4e46-80c1-41e7-9154-3181ccb36313.

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We investigate the action of the Atkin operator on spaces of overconvergent p-adic modular forms. Our contributions are both computational and geometric. We present several algorithms to compute the spectrum of the Atkin operator, as well as its p-adic variation as a function of the weight. As an application, we explicitly construct Heegner-type points on elliptic curves. We then make a geometric study of the Atkin operator, and prove a potential semi-stability theorem for correspondences. We explicitly determine the stable models of various Hecke operators on quaternionic Shimura curves, and

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Schill, Collberg Adam. "The last two digits of mk." Thesis, Linköpings universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-78532.

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In this thesis the last two digits of m^k, for different cases of the positive integers m and k, in the base of 10 has been determined. Moreover, using fundamental theory from elementary number theory and abstract algebra, results most helpful in finding the last two digits in any base b has been regarded and developed, such as how to reduce large m and k to more manageable numbers.

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Zhu, Dalin. "Residue number system arithmetic inspired applications in cellular downlink OFDMA." Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/2070.

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Arnold-Roksandich, Allison F. "There and Back Again: Elliptic Curves, Modular Forms, and L-Functions." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/61.

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Younes, Dina. "Využití systému zbytkových tříd pro zpracování digitálních signálů." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-233606.

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Předkládaná disertační práce se zabývá návrhem základních bloků v systému zbytkových tříd pro zvýšení výkonu aplikací určených pro digitální zpracování signálů (DSP). Systém zbytkových tříd (RNS) je neváhová číselná soustava, jež umožňuje provádět paralelizovatelné, vysokorychlostní, bezpečné a proti chybám odolné aritmetické operace, které jsou zpracovávány bez přenosu mezi řády. Tyto vlastnosti jej činí značně perspektivním pro použití v DSP aplikacích náročných na výpočetní výkon a odolných proti chybám. Typický RNS systém se skládá ze tří hlavních částí: převodníku z binárního kódu do RNS,

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Patel, Riyaz Aziz. "A study and implementation of parallel-prefix modular adder architectures for the residue number system." Thesis, University of Sheffield, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434492.

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Händel, Milene. "Circuitos aritméticos e representação numérica por resíduos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2007. http://hdl.handle.net/10183/12670.

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Este trabalho mostra os diversos sistemas de representação numérica, incluindo o sistema numérico normalmente utilizado em circuitos e alguns sistemas alternativos. Uma maior ênfase é dada ao sistema numérico por resíduos. Este último apresenta características muito interessantes para o desenvolvimento de circuitos aritméticos nos dias atuais, como por exemplo, a alta paralelização. São estudadas também as principais arquiteturas de somadores e multiplicadores. Várias descrições de circuitos aritméticos são feitas e sintetizadas. A arquitetura de circuitos aritméticos utilizando o sistema numé

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Books on the topic "Number system for modular arithmetic"

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1946-, Soderstrand Michael A., ed. Residue number system arithmetic: Modern applications in digital signal processing. Institute of Electrical and Electronics Engineers, 1986.

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Omondi, Amos R. Residue number systems: Theory and implementation. Imperial College Press, 2007.

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A, Soderstrand Michael, ed. Residue number system arithmetic: Modern applications in digital signal processing. IEEE Press, 1986.

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Moduli spaces and arithmetic dynamics. American Mathematical Society, 2012.

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Contemporary's number power: Fractions, decimals, and percents. Contemporary Books, 2000.

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Contemporary's number power: Addition, subtraction, multiplication, and division. Contemporary Books, 2000.

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Howett, Jerry. Contemporary's number power: A real world approach to math. McGraw-Hill/Wright Group, 2000.

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Jamīl, T̤āriq. Complex Binary Number System: Algorithms and Circuits. Springer India, 2013.

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Elliptic curves, modular forms, and their L-functions. American Mathematical Society, 2011.

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Contemporary's number power 2: Fractions, decimals and percents. Contemporary Books, 1988.

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Book chapters on the topic "Number system for modular arithmetic"

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Pirlo, Giuseppe. "Non-Modular Operations of the Residue Number System: Functions for Computing." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_3.

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Hunacek, Mark. "Congruences and Modular Arithmetic." In Introduction to Number Theory. Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003318712-3.

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Faltings, Gerd. "Arithmetic theory of Siegel modular forms." In Number Theory. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0072976.

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Lowry-Duda, David. "Visualizing Modular Forms." In Arithmetic Geometry, Number Theory, and Computation. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_19.

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Best, Alex J., Jonathan Bober, Andrew R. Booker, et al. "Computing Classical Modular Forms." In Arithmetic Geometry, Number Theory, and Computation. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_4.

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Frey, Gerhard, and Michael Müller. "Arithmetic of Modular Curves and Applications." In Algorithmic Algebra and Number Theory. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-59932-3_2.

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Arndt, Jörg. "Modular arithmetic and some number theory." In Matters Computational. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14764-7_39.

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Wiese, Gabor. "Computational Arithmetic of Modular Forms." In Notes from the International Autumn School on Computational Number Theory. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12558-5_2.

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Paliouras, Vassilis, and Thanos Stouraitis. "Logarithmic Number System." In Arithmetic Circuits for DSP Applications. John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119206804.ch7.

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Donnelly, Steve, and John Voight. "A Database of Hilbert Modular Forms." In Arithmetic Geometry, Number Theory, and Computation. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_12.

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Conference papers on the topic "Number system for modular arithmetic"

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Didier, Laurent-Stephane, Fangan-Yssouf Dosso, Nadia El Mrabet, Jeremy Marrez, and Pascal Veron. "Randomization of Arithmetic Over Polynomial Modular Number System." In 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH). IEEE, 2019. http://dx.doi.org/10.1109/arith.2019.00048.

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Meloni, Nicolas. "An Alternative Approach to Polynomial Modular Number System Internal Reduction." In 2022 IEEE 29th Symposium on Computer Arithmetic (ARITH). IEEE, 2022. http://dx.doi.org/10.1109/arith54963.2022.00024.

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Heinrich, Mark L., Ravindra A. Athale, Michael W. Haney, and Charles W. Stirk. "Design of a 16- × 16-bit digital optical multiplier using the residue number system." In OSA Annual Meeting. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.maa5.

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The residue number system (RNS) provides two main advantages to arithmetic computation: high dynamic range problems are subdivided into several independent modules of reduced dynamic range; and the arithmetic operations of addition, subtraction, and multiplication are performed in parallel with no carries between residue digits. Thus a high-accuracy multiplication can be divided into several medium-accuracy multiplications which can all be performed in parallel. Traditionally, m × m position-coded RNS look-up tables (LUTs) exhibit a spatial complexity (defined as the number of active elements)

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Lin, Shing-Hong. "An Optical Intensity and Polarization Coded Ternary Number System." In Spatial Light Modulators and Applications. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/slma.1988.the1.

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The lack of practical multiple-valued logic devices has in the past discouraged extensive investigation into multiple-valued logic. Recently, however, a number of optical processors have been presented to perform either multiple-valued logic functions[1,2], modified signed-digit arithmetic[3], or residue arithmetic[4]. Most of these implementations utilize position coding for the representation of residue numbers or multiple-valued numbers. For example, 9 pixels are needed to represent the combinations of two ternary inputs, and only one of the pixels will be turned ON at a time. As a result,

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Wei, Shugang. "Number conversions between RNS and mixed-radix number system based on Modulo (2p - 1) signed-digit arithmetic." In the 18th annual symposium. ACM Press, 2005. http://dx.doi.org/10.1145/1081081.1081124.

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Wei, Shugang. "Number Conversions between RNS and Mixed-Radix Number System Based on Modulo (2p - 1) Signed-Digit Arithmetic." In 2005 18th Symposium on Integrated Circuits and Systems Design. IEEE, 2005. http://dx.doi.org/10.1109/sbcci.2005.4286850.

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Heinrich, Mark L., Ravindra A. Athale, and Michael W. Haney. "Optical Outer Product Look-up Table Architectures for Residue Arithmetic." In Optical Computing. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/optcomp.1989.tuh1.

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The residue number system (RNS) allows high accuracy integer-valued arithmetic operations to be decomposed into independent (carry-free), low accuracy computations that can be performed in parallel. The RNS thus provides an attractive alternative to weighted number systems (e.g., binary or decimal) for high speed numerical computing1. The residue number representation is completely specified by a set of relatively prime moduli. The overall dynamic range is given by the product fo the moduli. Although this dynamic range can be arbitrarily high, the dynamic range required in any individual subca

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Kucherov, N., V. Kuchukov, E. Golimblevskaia, N. Kuchukova, I. Vashchenko, and E. Kuchukova. "Efficient implementation of error correction codes in modular code." In 3rd International Workshop on Information, Computation, and Control Systems for Distributed Environments 2021. Crossref, 2021. http://dx.doi.org/10.47350/iccs-de.2021.09.

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The article develops an efficient implementation of an algorithm for detecting and correcting multivalued residual errors with a fixed number of calculations of the syndrome, regardless of the set of moduli size. Criteria for uniqueness are given that can be met by selecting moduli from a set of primes to satisfy the desired error correction capability. An extended version of the algorithm with an increase in the number of syndromes depending on the number of information moduli is proposed. It is proposed to remove the restriction imposed on the size of redundant moduli. Identifying the locati

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Kucherov, N., M. Babenko, A. Tchernykh, V. Kuchukov, and I. Vashchenko. "Increasing reliability and fault tolerance of a secure distributed cloud storage." In The International Workshop on Information, Computation, and Control Systems for Distributed Environments. Crossref, 2020. http://dx.doi.org/10.47350/iccs-de.2020.16.

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The work develops the architecture of a multi-cloud data storage system based on the principles of modular arithmetic. This modication of the data storage system allows increasing reliability of data storage and fault tolerance of the cloud system. To increase fault-tolerance, adaptive data redistribution between available servers is applied. This is possible thanks to the introduction of additional redundancy. This model allows you to restore stored data in case of failure of one or more cloud servers. It is shown how the proposed scheme will enable you to set up reliability, redundancy, and

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Sorger, Volker J., Jiaxin Peng, Shuai Sun, Vikam K. Narayana, and Tarek El-Ghazawi. "Integrated Photonic Residue Number System Arithmetic." In Integrated Photonics Research, Silicon and Nanophotonics. OSA, 2018. http://dx.doi.org/10.1364/iprsn.2018.iw2b.3.

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Reports on the topic "Number system for modular arithmetic"

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Ostersetzer-Biran, Oren, and Jeffrey Mower. Novel strategies to induce male sterility and restore fertility in Brassicaceae crops. United States Department of Agriculture, 2016. http://dx.doi.org/10.32747/2016.7604267.bard.

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Abstract Mitochondria are the site of respiration and numerous other metabolic processes required for plant growth and development. Increased demands for metabolic energy are observed during different stages in the plants life cycle, but are particularly ample during germination and reproductive organ development. These activities are dependent upon the tight regulation of the expression and accumulation of various organellar proteins. Plant mitochondria contain their own genomes (mtDNA), which encode for rRNAs, tRNAs and some mitochondrial proteins. Although all mitochondria have probably evo

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