• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.765-789
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• 2017

Arithmetic is the basis of school mathematics and in fact, number and operation in elementary school curriculum is the most basic and essential domain. Even though there has been a consensus that arithmetic should be taught more meaningfully beyond the emphasis of calculation skills and teachers should emphasize the aspect of the arithmetical thinking, it is difficult to find studies which focus on the arithmetical thinking itself. So this research aims to explore the meaning of the arithmetical thinking and extract the arithmetical thinking factors. In order to solve the research problems, we reviewed and analyzed the literatures and then conducted Delphi survey to extract arithmetical thinking factors. From the results of this research, we found the meaning of arithmetical thinking and the arithmetical thinking factors. Especially, the arithmetical thinking consists of 18 factors. It is important to pay attention to students' arithmetical thinking because there are various factors of the arithmetical thinking. It is necessary to identify the aspects of arithmetical thinking reflected in school mathematics based on the meaning of arithmetical thinking and its factors. Based on this, it is possible to find effective teaching and learning methods of arithmetic focusing on the arithmetical thinking.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.675-681
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• 1989

As an adaptive control function generator, the CMAC (Cerebellar Model Arithmetic or Articulated Controller) based learning control has drawn a great attention to realize a rather robust real-time manipulator control under the various uncertainties. There remain, however, inherent problems to be solved in the CMAC application to robot motion control or perception of sensory information. To apply the CMAC to the various unmodeled or modeled systems more efficiently, It is necessary to analyze the effects of the CMAC control parameters an the trained net. Although the CMAC control parameters such as size of the quantizing block, learning gain, input offset, and ranges of input variables play a key role in the learning performance and system memory requirement, these have not been fully investigated yet. These parameters should be determined, of course, considering the shape of the desired function to be trained and learning algorithms applied. In this paper, the interrelation of these parameters with learning performance is investigated under the basic learning schemes presented by authors. Since an analytic approach only seems to be very difficult and even impossible for this purpose, various simulations have been performed with prespecified functions and their results were analyzed. A general step following design guide was set up according to the various simulation results.

• 한국기계연구소 소보
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• s.19
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• pp.125-139
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• 1989

As an adaptive control function generator, the CMAC (Cerebellar Model Arithmetic or Articulated Controller) based learning control has drawn a great attention to realize a rather robust real-time manipulator control under the various uncertainties. There remain, however, inherent problems to be solved in the CMAC application to robot motion control or perception of sensory information. To apply the CMAC to the various unmodeled or modeled systems more efficiently, it is necessary to analyze the effects of the CMAC control parameters on the trained net. Although the CMAC control parameters such as size of the quantizing block, learning gain, input offset, and ranges of input variables play a key role in the learning performance and system memory requirement, these have not been fully investigated yet. These parameters should be determined, of course, considering the shape of the desired function to be trained and learning algorithms applied. In this paper, the interrelation of these parameters with learning performance is investigated under the basic learning schemes presented by authors. Since an analytic approach only seems to be very difficult and even impossible for this purpose, various simulations have been performed with pre specified functions and their results were analyzed. A general step following design guide was set up according to the various simulation results.

• Journal of Communications and Networks
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• v.13 no.1
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• pp.1-5
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• 2011

Feedback with carry shift registers (FCSRs) over 2-adic number would be suitable in hardware implementation, but the are not efficient in software implementation since their basic unit (the size of register clls) is 1-bit. In order to improve the efficiency we consider FCSRs over $2^{\ell}$-adic number (i.e., FCSRs with register cells of size ${\ell}$-bit) that produce ${\ell}$ bits at every clocking where ${\ell}$ will be taken as the size of normal words in modern CPUs (e.g., ${\ell}$ = 32). But, it is difficult to deal with the carry that happens when the size of summation results exceeds that of normal words. We may use long variables (declared with 'unsigned _int64' or 'unsigned long long') or conditional operators (such as 'if' statement) to handle the carry, but both the arithmetic operators over long variables and the conditional operators are not efficient comparing with simple arithmetic operators (such as shifts, maskings, xors, modular additions, etc.) over variables of size ${\ell}$-hit. In this paper, we propose some conditions for FCSRs over $2^{\ell}$-adic number which admit fast software implementations using only simple operators. Moreover, we give two implementation examples for the FCSRs. Our simulation result shows that the proposed methods are twice more efficient than usual methods using conditional operators.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.3
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• pp.86-93
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• 2008

The multi-mode terminal modem which is capable of accommodating a variety of wireless communication standards needs versatile arithmetic units for processing a variety of word lengths and wide range of data rates. Since the target hardware is usually designed to meet the required highest performance, it is often wasteful in power consumption especially when low rate data processing cases. Thus, a speed and power adaptability of the arithmetic unit is a desirable feature for the wireless applications. In this paper, we propose a power efficient versatile adder architecture with carry skip logic as a basic building block constructed in hierarchical manner. The validity of the architecture is shown with respect to size, performance, and power efficiency in diverse operating modes.

• IEMEK Journal of Embedded Systems and Applications
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• v.12 no.1
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• pp.11-18
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• 2017

Finite field arithmetic has been extensively used in error correcting codes and cryptography. Low-complexity and high-speed designs for finite field arithmetic are needed to meet the demands of wider bandwidth, better security and higher portability for personal communication device. In particular, cryptosystems in GF($2^m$) usually require computing exponentiation, division, and multiplicative inverse, which are very costly operations. These operations can be performed by computing modular AB multiplications or modular $AB^2$ multiplications. To compute these time-consuming operations, using $AB^2$ multiplications is more efficient than AB multiplications. Thus, there are needs for an efficient $AB^2$ multiplier architecture. In this paper, we propose a low latency Montgomery $AB^2$ multiplier using redundant representation over GF($2^m$). The proposed $AB^2$ multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the proposed $AB^2$ multiplier saves at least 18% area, 50% time, and 59% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as exponentiation, division, and multiplicative inverse.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.10
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• pp.1794-1800
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• 2008

This paper presents a method of constructing the digital logic switching functions using PLA. First of all, we propose a MIN and MAX algebra arithmetic operation based on the Post algebra. And we discuss the T-gate which is used for realization of the MIN and MAX algebra arithmetic operation. Next, we discuss the MIN array and MAX array which are basic circuit of the PLA, also we discuss the literal property. For the purpose of the design for the digital logic switching functions using PLA, we Propose the variable partition, modular structure design, literal generator, decoder and invertor. The proposed method is the more compactable and extensibility.

• Journal of The Korean Association of Information Education
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• v.26 no.4
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• pp.285-293
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• 2022

The COVID-19 outbreak, which took longer than expected, caused considerable damage to students' basic academic ability in mathematics. In this paper, a multiplication table practice application that can help students improve their basic multiplication arithmetic skills has been developed based on a cloud-service. The performance of the application was improved by integrating the Flutter framework, Google Cloud, and Google Sheets. As a result of applying this application to 72 6th graders in elementary schools located in K Metropolitan City, for one week. students' spending time required for solving multiplication table problems was reduced by more than 28% compared to the initial period, while students' learning data was able to be accurately collected without errors. It is hoped that the development case conducted through the Flutter framework in this study can lead to the development of other educational learning applications.

• Asia-Pacific Journal of Business
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• v.4 no.2
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• pp.41-53
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• 2013

Undoubtedly, the basic sinking fund formula gives the future value of a series of equal installments. The main underlying assumption for using this formula is that installment and compounding frequency must be in equal interval. But when installment for a deposit scheme or any other savings scheme and compounding frequency do not occur in an equal interval, which is treated as the complex annuity problems in Finance Literature, the basic sinking fund formula does not give the accurate result. As a result, the obtainable amount from different deposit schemes offered by different banks and financial institutions does not match with the amount of future value calculated through the basic sinking fund formula by the investors or savers. This study focuses the concealed facts for such type of mismatches in values and at the same time it provides a solution through developing a new formula by extending the basic formula intended not only to remove those mismatches but also get the accurate future value from a sinking fund provision in case of complex annuity. Besides, since banks and financial institutions calculate the interest on the average amount of equal installments deposited within a period of time due to complex annuity, the study also formulates an arithmetic formula for calculating the average amount of installment.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.489-508
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• 2016

Number and operation is the most basic and crucial part in elementary mathematics but is also well known as a part that students have lots of difficulties. A lot of researches have been done in various ways to solve this problem but it can't be solved fundamentally by emphasizing calculation method and skill. So we need to go over it in terms of relevant arithmetical thinking. This study aims to diagnose the cause of an underachiever's difficulties about arithmetic and finds a prescription for her by analyzing her level of arithmetical thinking based on Guberman(2014) and understanding about arithmetic. To achieve this goal, we chose an 6th grader who's having a hard time particularly in number and operation among mathematics strands and conducted a case study carrying out arithmetical thinking level tests on two separate occasions and analyzing her responses. As a result of analyzing data, her arithmetical thinking corresponded to Guberman's first level and it is also turned out that student is suffering from some arithmetic concepts. We suggest several implications for teaching of arithmetic at elementary school in terms of the development of arithmetical thinking based on analysis result and discussion about it.