Subtraction Operations Research Articles

Channel and Spatial Enhancement Network for human parsing

The dominant backbones of neural networks for scene parsing consist of multiple stages, where feature maps in different stages often contain varying levels of spatial and semantic information. High-level features convey more semantics and fewer spatial details, while low-level features possess fewer semantics and more spatial details. Consequently, there are semantic-spatial gaps among features at different levels, particularly in human parsing tasks. Many existing approaches directly upsample multi-stage features and aggregate them through addition or concatenation, without addressing the semantic-spatial gaps present among these features. This inevitably leads to spatial misalignment, semantic mismatch, and ultimately misclassification in parsing, especially for human parsing that demands more semantic information and more fine details of feature maps for the reason of intricate textures, diverse clothing styles, and heavy scale variability across different human parts. In this paper, we effectively alleviate the long-standing challenge of addressing semantic-spatial gaps between features from different stages by innovatively utilizing the subtraction and addition operations to recognize the semantic and spatial differences and compensate for them. Based on these principles, we propose the Channel and Spatial Enhancement Network (CSENet) for parsing, offering a straightforward and intuitive solution for addressing semantic-spatial gaps via injecting high-semantic information to lower-stage features and vice versa, introducing fine details to higher-stage features. Extensive experiments on three dense prediction tasks have demonstrated the efficacy of our method. Specifically, our method achieves the best performance on the LIP and CIHP datasets and we also verify the generality of our method on the ADE20K dataset.

Arithmetic Proficiency of Pre-Service Science Teachers: An Empirical Study

Mastery of arithmetic operations is fundamental for students pursuing science education, as these skills are essential in solving complex problems in physics, chemistry, and biology. However, gaps in students' arithmetic proficiency can hinder their academic and professional development. This study aims to examine the arithmetic skills of pre-service science teachers in solving mathematical problems across six domains: addition, subtraction, multiplication, division, exponentiation, and mixed operations. A total of 37 short-answer questions were administered, and the results were analyzed by domain. The findings indicate that students demonstrate proficiency in basic operations involving whole numbers, particularly in addition and subtraction. However, challenges persist in the areas of fractions, decimals, and mixed operations, where accuracy rates were notably lower. These gaps in understanding may affect students' ability to apply mathematical concepts in their science courses and future teaching roles. The study's limitations include a focus on quantitative results without exploring the cognitive processes behind student errors. Future research should investigate intervention strategies to address these weaknesses, potentially through targeted instructional approaches or the use of technology to enhance learning outcomes

ANALYSIS OF STUDENTS' UNDERSTANDING OF MATHEMATICAL CONCEPTS ON FRACTIONS IN GRADE VIII AT SMP NEGERI 2 MAZINO

This study aims to describe and identify the factors contributing to the low understanding of mathematical concepts related to fractions among students. This research is qualitative in nature with a descriptive approach. The informants in this study are 18 eighth-grade students from SMP Negeri 2 Mazino. Data were analyzed through the steps of data reduction, data presentation, and conclusion drawing. The data collection techniques used are tests and interviews. The results show that, overall, students exhibit low understanding of concepts when distinguishing between two fractions, with 18% categorized as very poor. In classifying fractions by type, the percentage is 19% in the very poor category. For ordering fractions from smallest to largest, the percentage is 37%, categorized as poor. In simplifying addition and subtraction operations involving fractions, 22% fall into the poor category. Additionally, in relating everyday life to fraction concepts, the percentage is 60%, categorized as sufficient, while 20% fall into the very poor category. Factors influencing this include a lack of understanding of the statements in the tests, not comprehending the questions posed, being less meticulous in understanding simple fractions, and difficulty in interpreting word problems related to fraction operations. In conclusion, eighth-grade students at SMP Negeri 2 Mazino demonstrate low understanding in completing tests on fractions. It is recommended that teachers create a question-and-answer space in their lesson plans to enhance students' conceptual understanding when working with fractions.

Efficient simultaneous migration of primary and free-surface related multiples using reformulated two-way wave-equation depth extrapolation scheme

The migration of free-surface related multiples can enhance subsurface illumination and improve overall imaging quality. However, this process encounters two main challenges: crosstalk artefacts resulting from the cross-correlation of non-reflection-related wavefields, and the increased computational burden of imaging different orders of multiples. We propose a novel method that simultaneously and efficiently migrates both primary and multiple reflections while mitigating crosstalk artefacts. The method employs a reformulated two-way wave-equation depth extrapolation scheme that simplifies up/down wavefield separation through straightforward summation and subtraction operations at each depth step. Two innovative algorithms are integrated into this scheme: a generalized up/down separation algorithm, and a simultaneous migration algorithm of primary and free-surface-related multiples. The up/down separation algorithm efficiently separates the up- and down-going wavefields into primary wavefield and multiple reflections of various orders at the measurement surface. The simultaneous migration algorithm then pairs these components as two-way quantities, allowing for efficient depth extrapolation using a unified propagator, followed by effective decomposition into corresponding one-way components for imaging. Numerical experiments conducted on synthetic models, including a two-dimensional two-layer model and the Sigsbee 2B model, as well as on real seismic data from a gas hydrates bearing zone, demonstrate that the proposed method simultaneously migrate both primary and multiple reflections with reduced crosstalk artefacts and limited computational overhead.

Development of Algebra Test Using the Item Response Theory Approach for Junior High School Students

This research aims to develop valid and reliable measuring tool for students' algebraic abilities that can be used in schools and the general public. The research follows a structured test development design, including stages such as preparing test specifications and items, field testing, revising items, and test development. The questions are aligned with the 2013 curriculum syllabus, ensuring relevance to educational standards. The test was given to 662 junior high school students in Kendari City, Indonesia, and their responses were analyzed using the item response theory (IRT) model with two logistic parameters: item difficulty level and item discriminatory power. The BILOG MG program was employed to estimate item and ability parameters. Before conducting item analysis with IRT, essential assumption tests were conducted, including unidimensional and model fit tests. The results of the development process, based on item analysis using BILOG MG, yielded 15 items covering various aspects of algebraic abilities. These items were derived from indicators such as recognizing algebraic forms, identifying elements within these forms, performing addition, subtraction, multiplication, and division operations on algebraic forms, presenting and solving real-world problems in algebraic contexts, and addressing contextual problems involving algebraic operations. The items demonstrated good fit with the model and exhibited an appropriate level of item difficulty and discriminatory power, making them suitable for use as a reliable assessment tool. Consequently, these developed tests are deemed effective for measuring students' foundational algebraic abilities.

Upaya Meningkatkan Kemampuan Berhitung Melalui Media Pembelajaran Papan Jurang Pada Siswa Kelas II SD YPK Bethania Mariadei

Based on the results of interviews conducted with grade 2 teachers of YPK Bethania Mariadei Elementary School, it was obtained that students still had difficulty in understanding the material on addition and subtraction operations (borrowing and without borrowing). After conducting initial observations to measure students' initial abilities, the following information was obtained: 1) 2 students out of 21 students with a percentage of 9.5% obtained scores above or reaching the KKM, 2) 19 students out of 21 students with a percentage of 90.5% had not obtained scores reaching the KKM. As for the minimum completion score in Mathematics, it is 60 with a success indicator of ≥ 75%. The purpose of this study is to improve students' addition and subtraction arithmetic skills through the use of the cliff board learning media (addition and subtraction). This study uses a classroom action research method. Data collection was taken using a learning outcome test on the ability to count addition and subtraction arithmetic and observations for teacher and student activities using qualitative and quantitative analysis. The results achieved after implementing the ravine board media (addition and subtraction) are that in learning activities it was found that there was an increase in student abilities above the KKM in cycle I reaching 42.9% while in cycle II it reached 86%. So it can be concluded that the application of the ravine board learning media (addition and subtraction) can improve the ability to calculate addition and subtraction in grade 2 students of YPK Bethania Mariadei Elementary School

Designed activities on developing mental strategies using alms value-based learning trajectory in elementary school

Mental strategies are recognized as an effective approach for solving arithmetic operations such as addition and subtraction. This study focuses on developing and implementing instructional activities aimed at enhancing students' mental strategy skills through the Indonesian Realistic Mathematics Education (IRME) approach. The research employed a design-based methodology involving 2nd-grade students from an Islamic-integrated school in Surabaya. The study followed a research design that emphasizes the development of local instructional theory, encompassing three key phases: the preparatory phase (initial design development), the experimental phase (classroom teaching experiments), and the retrospective analysis phase. Data collection methods included documentation, field notes, and interviews. In the first trial, three instructional activities were conducted. Based on the analysis of the first trial, the number of activities in the second trial was increased to four: "Let's Get Used to Alms Every Day," "Don't Forget Routine Alms This Week," "Set Your Own Pocket Money," and "Let's Give Away Your Alms to Break Mr. Samad’s Fast." These activities were designed to achieve specific mathematical objectives, enabling students to understand and solve addition and subtraction problems using strategies such as skip counting, borrowing, and saving. The retrospective analysis concluded that students successfully learned to perform addition and subtraction operations on both monetary values and ordinary numbers within the designed learning trajectory.

Sosialisasi Media Aritmatika Sempoa Pada Orang Tua Anak

The abacus is a traditional calculating tool from Southeast Asia such as China, Korea, Taiwan and Japan. According to Chen (2009), it is said that the abacus existed in Babylonia and China around 2400 BC and 300 BC. In education in Indonesia in the 1990s the abacus began to enter the form of arithmetic courses, after 700 years of disappearance. The impact of the abacus is amazing, a kindergarten child who masters mathematics can calculate faster than a calculator. The abacus succeeded in attracting the attention of mothers with small children, who then enrolled their children in abacus arithmetic courses. This program is very appropriate for children aged kindergarten to elementary school. The conditions that occurred in RW 01, Gedong Village, the proposing team found that there were still many children who had difficulty using addition, subtraction operations, or using the abacus. Parents don't even understand how to use the abacus in calculating. Maybe this is because there are no parents to teach their children, because the majority of children in RW 01 are from the lower middle class. To overcome the problems mentioned above, the solution offered in this community service is to provide socialization on abacus arithmetic media to parents of children in the RW 01 Gedong Village environment, in order to optimize children's potential, including: increasing the ability to calculate faster, balancing the use of left and right brain and optimizing it to achieve a level of analytical thinking and correct analytical thinking, training concentration thinking power, helping children to master other subjects, developing imagination so that children's creativity develops, and getting used to numbers makes children not I'm afraid of exact lessons

PENGEMBANGAN MEDIA ARISAN ANTIK PADA PEMBELAJARAN BILANGAN BULAT DI KELAS INKLUSI SD SWASTA AL-AZHAR BUKITTINGGI

Making this innovative work aims to increase motivation and student learning outcomes in learning negative and positive integers by using Antique Arisan media (Manual and Electric Number Lines). This innovative work is the development of a number line media made using a board with an attractive appearance using green led lights on positive integers, red led lights on negative integers, each number is embossed for students with special needs, namely the blind and low vision. How to operate this media in two ways. (1) Use of this media by pressing the switch for each number to be addressed to complete simple number operations such as addition and subtraction of negative and positive integers. (2) Using a rail equipped with a toy that moves forward to show the addition of numbers, moves backwards for integer subtraction operations, this rail is installed under the number line which functions as a substitute for carrying out negative and positive integer operations using the number line, if the use of lights cannot be used because there is no power source. This use helps regular students and especially students with special needs in adding and subtracting negative and positive integers, so that students with special needs are served according to their needs and can solve problems encountered related to adding and subtracting integers, so that learning outcomes can increase.

Phase estimation via multi-photon subtraction inside the SU(1,1) interferometer

To improve the phase sensitivity, multi-photon subtraction schemes (multi-PSS) within the SU(1,1) interferometer are proposed. The input states are the coherent state and the vacuum state, and the detection method is homodyne detection. The effects of multi-photon subtraction on phase sensitivity, quantum Fisher information (QFI), and quantum Cramér-Rao bound (QCRB) are analyzed under both ideal and photon losses situations. It is shown that the internal subtraction operation can improve the phase sensitivity, which becomes better performance by increasing subtraction number. It can also efficiently improve the robustness of the SU(1,1) interferometer against internal photon losses. By comparing separatively arbitrary photon subtraction on the two-mode inside SU(1,1) interferometer, the performance differences under different conditions are analyzed, including the asymmetric properties of non-Gaussian operations on the phase precision and the QFI. Our proposed scheme represents a valuable method for achieving quantum precision measurements.

Peningkatan Kemampuan Berpikir Kritis Siswa Kelas III Pada Materi Operasi Pengurangan Model Teams Games Tournament

This research aims to improve the learning outcomes and critical thinking abilities of class III students on subtraction operations material through the application of the Tems Gemes Tournament learning model. This type of research uses Class Action (PTK) which is carried out in 2 cycles. The data collection techniques used are planning, implementation, observation and reflection. The object of this research was class III students at SDN Pangendisan, totaling 16 students. The instruments in this research used observation, interviews and tests. This research shows that the application of the Teams Games Tournament model can improve students' learning outcomes and critical thinking abilities. The results of this research obtained that the average student learning outcomes in the pre-cycle were 23.9%, then increased in the first cycle to 70.24% with (KKM) of 67% and again increased in the second cycle, namely 83.57 with the category ( KKM) of 86%. With the learning results, it can be shown that students' thinking abilities in implementing the Teams Games Tournament model become more active, involved and able to solve mathematical problems. Thus, the Tems Games Tournament learning model improves learning outcomes and students' critical thinking skills in subtraction operations material. Based on the research results, it can be concluded that the Teams Games Tournament learning model can improve the Mathematics learning abilities of class III students at SDN Pangendisan.

Students’ understanding of vector operations: With and without physics education technology simulation

This study aims to investigate the influence of technology integration (physics education technology simulation) in physics learning. A quantitative method with a quasi-experimental post-test-only design was applied to reveal the differences in students’ abilities to operate vectors between the group that learned and tested using simulation and the group that learned using graphics only. The test consisted of 16 questions on the addition and subtraction of two vectors divided into one and two dimensions. Student response data were analyzed using descriptive statistics and Kruskal-Wallis test. The analysis results show that the vector operation score for experimental group 1, which learned vector operations through graphic learning using simulation and tested with the same simulation (86.15), is higher than experimental group 2, which learned vector operations through graphic learning using simulation (76.59), and the control group, which learned vector operations through graphic learning without simulation assistance (71.81). All three groups have higher average scores for one-dimensional than two-dimensional vector operations. They also have higher average scores for vector addition compared to vector subtraction operations. Kruskal-Wallis test results indicate a significant difference in the average vector operation scores for the three groups (ρ=0.021). This suggests that integrating technology in the learning and testing processes leads to a significant difference. Moreover, the difference is significant for one-dimensional vector operations (ρ=0.004) and not significant for two-dimensional vector operations (ρ=0.107). These findings could support the implementation of similar approaches at the university and high school levels, especially for vector-related topics, in both learning and testing processes.

Analisis Kesulitan Siswa Belajar Matematika pada Materi Operasi Penjumlahan dan Pengurangan pada Bilangan Cacah Kelas II di SDN 1 Demulih

This research aims to find out the problems that make it difficult for students to learn the material on addition and subtraction operations in class II whole numbers at SDN 1 Demulih. This research focuses on answering questions related to how difficult it is for students to learn the material on addition and subtraction operations in class II whole numbers at SDN 1 Demulih. To answer this question, this research uses qualitative research using qualitative descriptive methods. The data collection used is observation, interviews and documentation. Meanwhile, in analyzing the data, researchers used quantitative descriptive analysis techniques. The results of this study found that class II students at SDN 1 Demulih experienced learning difficulties with the percentage of learning difficulties including 75% in understanding the concept of place value, 66.67% in addition procedures using saving techniques, 79.17% in the concept of "borrowing" in subtraction operations. , 83.33% in subtraction procedures with borrowing techniques, and 70.83% in understanding word problems related to addition and subtraction operations.

Use of Ice Cream Stick Props to Improve Mathematics Learning Outcomes Addition and Subtraction Material For Grade I Students of MI Hidayatul Mubtadiin New

The background of this research was – low mathematics calculation operations, addition, and subtraction in mathematics subjects found in the learners at Islamic Primary School Hidayatul Mubtadiin New Kedungwungu. This Classroom Action Research applied the Kemmis & Taggar model, starting from planning, acting, observing, and reflecting to improve the mathematics learning outcomes of the learners. The population consisted of first graders of Islamic Primary School Hidayatul Mubtadiin New who could not do addition and subtraction operations. The population also became the research sample that received mathematics learning with ice cream stick properties for three cycles. The researchers collected the data using Observation, tests, documentation, and interviews to analyze descriptively. The results showed increased learning outcomes for the learners after using the ice cream stick property for learning mathematics within the materials of addition and subtraction. The results showed that the learners could reach the minimum mastery completion on each cycle. In cycle I, six learners, or 30% of learners, passed the minimum completion. In cycle II, the numbers increased to 13 learners, 65%. Then, in cycle III, the numbers improved to 17 learners, 85%. From the results, the researchers suggested schools provide proper property facilities and infrastructure for the teachers. The researchers also recommend that teachers apply the ice cream stick property to mathematics learning. The teachers must also consider the learners' skills.

Development Paillier's library of fully homomorphic encryption

One of the new areas of cryptography considered-homomorphic cryptography. The article presents the main areas of application of homomorphic encryption. An analysis of existing developments in the field of homomorphic encryption carried out. The analysis showed that existing library implementations only allow processing bits or arrays of bits and do not support division and subtraction operations. However, to solve applied problems, support for performing integer operations are necessary. Because of the analysis, the need to implement the homomorphic division and subtraction operations identified, as well as the relevance of developing our own implementation of a homomorphic encryption library over integers. The ability to perform four operations (addition, difference, multiplication and division) on encrypted data will expand the areas of application of homomorphic encryption. A homomorphic division and subtraction methods proposed that allows the division operation performed on homomorphically encrypted data. An architecture for a library of fully homomorphic operations on integers is proposed. The library supports basic homomorphic operations on integers, as well as homomorphic division method. The article also provides measurements of the time required to perform certain operations on encrypted data and analyzes the efficiency of the developed implementation of the library.

Dienes block media assisted by mathematical worksheets to improve student learning outcomes: Teacher action research

The development of science has shifted the process of learning mathematics from previously only involving numbers to numbers that have meaning, one of which is in the form of stories. However, many problems still need to be solved with the concept of addition and subtraction in the form of story problems. This research aims to improve student learning outcomes in addition and subtraction material through story problems. This research used the Teacher Action Research (TAR) approach with 14 second-grade students at Ciren Elementary School, Indonesia as participants. This research also used two data collection methods: providing mathematical worksheets and observations carried out by special observers. Data analysis was carried out by looking at the mean student scores, reflecting through FGDs with observers, and filling in observation sheets by the teacher. Furthermore, the results of this research are presented in the form of teacher observation sheet scores and mathematical worksheet work results. The score results on the observation sheet show an increase in scores from learning in cycle 1 to cycle 2. In addition, the average score of students' mathematical worksheets after intervention in the form of dienes block media and mathematical worksheets always increases with pre-cycle details (48), cycle I (80), and cycle II (84). Thus, using dienes block media assisted by mathematical worksheets can have direct implications for improving mathematics learning in addition and subtraction operation material.

A Prototype-Based Neural Network for Image Anomaly Detection and Localization

Image anomaly detection and localization perform not only image-level anomaly classification but also locate pixel-level anomaly regions. Recently, it has received much research attention due to its wide application in various fields. This paper proposes ProtoAD, a prototype-based neural network for image anomaly detection and localization. First, the patch features of normal images are extracted by a deep network pre-trained on nature images. Then, the prototypes of the normal patch features are learned by non-parametric clustering. Finally, we construct an image anomaly localization network (ProtoAD) by appending the feature extraction network with L2 feature normalization, a 1×1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\ imes 1$$\\end{document} convolutional layer, a channel max-pooling, and a subtraction operation. We use the prototypes as the kernels of the 1×1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\ imes 1$$\\end{document} convolutional layer; therefore, our neural network does not need a training phase and can conduct anomaly detection and localization in an end-to-end manner. Extensive experiments on two challenging industrial anomaly detection datasets, MVTec AD and BTAD, demonstrate that ProtoAD achieves competitive performance compared to the state-of-the-art methods with a higher inference speed. The code and pre-trained models are publicly available at https://github.com/98chao/ProtoAD.

Indirect frequency estimation by time-shifted accelerations subtraction: Generalization of the methodology and numerical application on a Warren truss bridge

In the context of Structural Health Monitoring (SHM) of transportation infrastructures, bridge eigen frequencies are commonly adopted as diagnostic indices. Under this regard, as a cost-effective identification methodology, indirect SHM, which consists in the use of sensors installed on running vehicles, is attracting attention. In particular, methods relying on the use of two or more on-board sensors may suppress the influence of track irregularity, which is a remarkable drawback for indirect SHM, and improve the identification accuracy. However, the combination characteristics of the two on-board sensors is still an open issue to be addressed. Also, in many studies, test bridges consist of simple girders, and there are few verifications on complex structures, such as truss bridges. The first contribution of this study is the analytical and generalized expression of the operational range defining the use of time-shifted signals subtraction operation for indirect frequency estimation. After the outcomes provided by this formulation were confirmed by the results obtained from a 2D explanatory example, the proposed procedure was further validated through three-dimensional train-track-bridge dynamic simulations. For this purpose, 3D FE model of a real existing Warren truss bridge, dynamically validated through experimental tests, and a 3D multi-body rail vehicle were adopted. From an engineering standpoint, a relevant result of this study found is that the coexistence of proper sensors onboard positioning and sufficient target bridge component excitation revealed to be crucial for the success of an indirect frequency identification procedure which is based on time-shifted accelerations subtraction.

Target localization image encryption of wind turbines based on DNA strand replacement rule

The continuous development of the industrial internet of things has raised increasingly high requirements for the secure storage and transmission of information. Ensuring that image information avoids malicious attacks and tampering during transmission has become an important aspect of information security. In response to the security requirements for drone-captured image transmission during wind turbine inspection, this paper proposes a new target localization encryption scheme based on DNA strand replacement rules. In traditional methods using DNA encryption, the DNA computing rules used include DNA addition, DNA subtraction, and DNA XOR operations. These operations are relatively simple and have weak biological relevance, making them vulnerable to attack and decryption. To address this issue, this article introduces the principle of DNA strand replacement reaction and proposes a DNA strand displacement reaction rule. The rule has stronger biological relevance and more complex operational rule than traditional DNA algorithms, thus providing stronger security for encrypted images. Experimental results indicate that this encryption algorithm effectively enhances the information security of ciphertext images and can withstand brute-force attacks and various statistical attacks.

METHOD FOR DETERMINING THE BIT GRID OVERFLOW OF A COMPUTER SYSTEM OPERATING IN THE SYSTEM OF RESIDUAL CLASSES

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.