METHOD FOR DETERMINING THE BIT GRID OVERFLOW OF A COMPUTER SYSTEM OPERATING IN THE SYSTEM OF RESIDUAL CLASSES
DOI:
https://doi.org/10.15588/1607-3274-2024-1-21Keywords:
arithmetic operation of modular addition, bit grid overflow, comparison operation, computer system, nonpositional code, rank of the number, system of residual classes, zeroing procedureAbstract
Context. Consideration of a set of examples of practical application of the procedure for identifying overflow of the bit grid of a computer system operating in a non-positional number system in residual classes. The object of the study is the process of processing data represented in the residual class system.
Objective. The goal of the work is to consider and analyze examples of the bit grid overflow definition of a computer system when implementing the operation of adding two numbers in a system of residual classes based on the application of a method for determining the bit grid overflow, based on the use of the concept of number rank.
Method. The specificity of the functioning of a computer system in a system of residual classes requires the implementation of not only modular operations, but also requires the implementation of additional, so-called non-modular operations. Non-modular operations include the operation of determining the overflow of the bit grid of a computer system in the system of residual classes. In a non-positional number system in residual classes, implementing the process of detecting overflow of the bit grid of a computer system is a difficult task to implement. The method considered in the work for determining the overflow of the bit grid is based on the use of positional features of a non-positional code of numbers in the system of residual classes, namely the true and calculated ranks of a number. The process of determining the overflow of the result of the operation of adding two numbers in the system of residual classes has been studied, since this arithmetic operation is the main, basic operation performed by a computer system.
Results. The developed methods are justified theoretically and studied when performing arithmetic modular operations of addition, subtraction and multiplication using tabular procedures.
Conclusions. The main advantage of the presented method is that the process of determining the overflow of the bit grid can be carried out in the dynamics of the computing process of the computer system, i.e. without stopping the solution of the problem. This circumstance makes it possible to reduce the unproductive expenditure of the computer system in the system of residual classes. In addition, this method can be used to control the operation of adding two numbers in the residual class system. This increases the reliability of obtaining the true result of the operation of adding two numbers in the system of residual classes.
References
Akushskij I. Ya., Yudickij D. I. Mashinnaya arifmetika v ostatochnyx klassax. Mosсow, Sovet. radio, 1968, 440 p.
Krasnobayev V., Yanko A., Hlushko A. Information Security of the National Economy Based on an Effective Data Control Method, Journal of International Commerce, Economics and Policy, 2023, No. 14(3), Article no. 2350021. DOI: 10.1142/S1793993323500217
Butt M. A., Ajmal Z., Khan Z. I. , Idrees M., Javed Y. An InDepth Survey of Bypassing Buffer Overflow Mitigation Techniques, Applied Sciences, 2022, No. 12(13), P. 6702. DOI: 12. 6702. 10.3390/app12136702
Gavrylenko S. Y., Chelak V. V., Semenov S. G. Development of method for identification the computer system state based on the decision tree with multi-dimensional nodes, Radio Electronics, Computer Science, Control, 2022, No. (2), pp. 113–121. DOI: https://doi.org/10.15588/1607-3274-2022-2-11
Laktionov O., Lievi L., Tretia A., Movin M. Investigation of combined ensemble methods for diagnostics of the quality of interaction of human-machine systems, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 2023, No. 4, pp. 138–143. DOI: https://doi.org/10.33271/nvngu/2023-4/138
Salnikov D., Karaman D., Krylova V. Highly reconfigurable soft-CPU based peripheral modules design, Advanced Information Systems, 2023, No. 7(2), pp. 92–97. DOI: https://doi.org/10.20998/2522-9052.2023.2.13
Yanko A., Koshman S., Krasnobayev V. Algorithms of data processing in the residual classes system, International Scientific-Practical Conference: Problems of Infocommunications. Science and Technology (PIC S&T). Kharkov, 2017, pp. 117– 121. DOI: 10.1109/INFOCOMMST.2017.8246363
Torgashev V. A. Sistema ostatochnyx klassov i nadezh-nost' CVM. Moscow, Sovet. radio, 1973, 118 p.
Mohan P. V. A. Residue Number Systems: Theory and Applications. Birkhäuser Basel, Springer International Publishing, Switzerland, 2016, 351 p. DOI: 10.1007/978-3-319-41385-3_2 9
Colbert I., Pappalardo A., Petri-Koenig J. A2Q: AccumulatorAware Quantization with Guaranteed Overflow Avoidance Supplementary Material, 2023 IEEE/CVF International Conference on Computer Vision (ICCV). Paris, France, 2023, pp. 16943–16952. DOI: 10.1109/ICCV51070.2023.0155
Bo L., Ruifeng Z., Jiangang L., Wenxin G., Yang L. Control on Abnormal Data Overflow of Distribution Network Management Platform, Journal of Physics: Conference Series 1748, 2021, No. 032064, pp. 1–5. DOI: 10.1088/1742-6596/1748/3/032064
Meakin R. L. Adaptive spatial partitioning and refinement for overset structured grids, Computer Methods in Applied Mechanics and Engineering, 2000, No. 189 (4), pp. 1077–1117. DOI: https://doi.org/10.1016/S0045-7825(99)00369-2
Hui H. W., Zhou C. C., Xu S. G., Lin F. H. A Novel Secure Data Transmission Scheme in Industrial Internet of Things, China Communications, 2020, No. 17 (1), pp. 73–88. DOI: 10.23919/JCC.2020.01.006
Chiamwongpaet S., Piromsopa K. Boundary Bit: Architectural Bound Checking for Buffer-Overflow Protection, ECTI Transactions on Computer and Information Technology (ECTI-CIT), 2020, No. 14, pp. 162–173. DOI:10.37936/ecticit.2020142.212338
Tsukada M., Matsutani H. An Overflow/Underflow-Free FixedPoint Bit-Width Optimization Method for OS-ELM Digital Circuit, IEICE Trans. Fundamentals, Vol. E105–A, No. 3, 2022, pp. 437–447. DOI: 10.1587/transfun.2021VLP0017
Xie H., Song Y., Cai L., Li M. Overflow Aware Quantization: Accelerating Neural Network Inference by Low-bit MultiplyAccumulate Operations, 29th International Joint Conference on Artificial Intelligence. Japan, 2020, pp. 868–875. DOI: https://doi.org/10.24963/ijcai.2020/121
Lee S., Shin D. J. Overflow-Detectable Floating-Point Fully Homomorphic Encryption, IEEE Access, 2024, pp. 1–21. DOI: 10.1109/ACCESS.2024.3351738
Li T., Wang Y., Li R., Li K. A bidirectional overflow digital correction algorithm with a single bit redundancy used in the pipeline A/D converters, 2009 IEEE 8th International Conference on ASIC. Changsha, Hunan, 2009, pp. 238–241. DOI: 10.1109/ASICON.2009.5351482
Cha Y., Cho G., Choi H., Song H. N bit result integer multiplier with overflow detector, Electronics Letters, 2001, No.(37), pp. 940–942. DOI: 10.1049/el:20010633.
Ivohin E. V. Gavrylenko V. V., Ivohina K. E. On the recursive algorithm for solving the traveling salesman problem on the basis of the data flow optimization method, Radio Electronics, Computer Science, Control, 2023, No. (3), pp. 141–147. DOI: https://doi.org/10.15588/1607-3274-2023-3-14
Ulman Z., Czyzak M. and Zurada J. Effective RNS scaling algorithm with the Chinese remainder theorem decomposition, Proceedings of IEEE Pacific Rim Conference on Communications Computers and Signal Processing, 1993, Vol. 2, pp. 528– 531 DOI: 10.1109/PACRIM.1993.407305
Krasnobayev V. A., Yanko A. S., Kovalchuk D. M. 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, 2022, No. 4, pp. 18–27. DOI: https://doi.org/10.15588/1607-3274-2022-4-2
Subbotin S. A. Data clustering based on inductive learning of neuro-fuzzy network with distance hashing, Radio Electronics, Computer Science, Control, 2022, No. 4, pp. 71–85. DOI: https://doi.org/10.15588/1607-3274-2022-4-6
Krasnobayev V. Koshman S., Yanko A., Martynenko А. Method of Error Control of the Information Presented in the Modular Number System, International Scientific-Practical Conference: Problems of Infocommunications Science and Technology (PIC S&T). Kharkov, 2018, pp. 39–42. DOI: 10.1109/INFOCOMMST.2018.8632049
Chao Huang, Peterson D., Rauch H., Teague J., Fraser D. Implementation of a fast digital processor using the residue number system, IEEE Transactions on Circuits and Systems, 1981, January, Vol. 28, № 1, pp. 32–38. DOI: 10.1109/TCS.1981.1084905
Szabo N. S., Tanaka R. I. Residue Arithmetic and Its Applications to Computer Technology. New York, McGraw-Hill, 1967, 236 p.
Piestrak S. J. Design of residue generators and multioperand modular adders using carry-save adders, Proceedings 10th IEEE Symposium on Computer Arithmetic, 26–28 June, 1991, pp. 100–107. DOI: 10.1109/ARITH.1991.145540
Salnikov D., Karaman D., Krylova V. Highly reconfigurable soft-CPU based peripheral modules design, Advanced Information Systems, 2023, No. 7(2), pp. 92–97. DOI: https://doi.org/10.20998/2522-9052.2023.2.13
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 A. S. Yanko, V. A. Krasnobayev, S. B. Nikolsky, O. O. Kruk
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
-
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
-
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
-
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
