• Proceedings of the IEEK Conference
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• 2003.07b
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• pp.835-838
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• 2003

본 논문에서는 현재 MPEG, JPEG 압축 알고리즘에서 쓰이는 DCT(Discrete Cosine Transform)기반의 손실 영상 압축에 사용되는 양자화(Quantization) 처리에 필요한 나눗셈 연산기를 제안한다. 영상 데이터 처리를 위한 양자화기(Quantizer)는 DCT로부터 매 사이클마다 영상 데이터를 입력 받아 양자화 처리를 해야하며 보다 나은 영상 데이터를 위해 최종 나눗셈 결과 즉, 몫을 소수 첫째자리에서 반올림(Rounding)해야 한다. 이를 위해 반올림 동작이 추가된 Pipelined Nonrestoring Array Divider를 설계하였다. 제안된 방법의 타당성을 검증하기 위해 DCT로부터 나온 영상 데이터를 제안된 구조의 양자화기로 양자화하여 일반 양자화기에서 나온 압축된 데이터와 비교해 보았다. 또한 합성기(Synthesis)를 통하여 실제 하드웨어 크기를 분석하였다.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.221-242
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• 2006

For teaching division more effectively, it is necessary to know students' informal knowledge before they learned formal knowledge about division. The purpose of this study is to research students' informal knowledge of division and to analyze meaningful suggestions to link formal knowledge of division in elementary school mathematics. According to this purpose, two research questions were set up as follows: (1) What is the students' informal knowledge before they learned formal knowledge about division in elementary school mathematics? (2) What is the difference of thinking strategies between students who have learned formal knowledge and students who have not learned formal knowledge? The conclusions are as follows: First, informal knowledge of division of natural numbers used by grade 1 and 2 varies from using concrete materials to formal operations. Second, students learning formal knowledge do not use so various strategies because of limited problem solving methods by formal knowledge. Third, acquisition of algorithm is not a prior condition for solving problems. Fourth, it is necessary that formal knowledge is connected to informal knowledge when teaching mathematics. Fifth, it is necessary to teach not only algorithms but also various strategies in the area of number and operation.

• Education of Primary School Mathematics
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• v.25 no.3
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• pp.251-278
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• 2022

The purpose of this study is to obtain implications for mathematical education by analyzing how the multiplication and division of decimal numbers are presented in the elementary mathematics textbooks in Korea, Japan, Singapore, and Finland. Compared to the fact that students often have misconceptions about multiplication and division of decimal numbers, there have been not many comparative studies in recent elementary mathematics textbooks. For this study, we selected elementary mathematics textbooks those are widely used in Japan, Singapore, and Finland along with Korean elementary mathematics textbooks. We chose the textbooks because the students in the selected countries have scored high in international achievement studies such as TIMSS and PISA. The analysis was examined in terms of elementary mathematics curriculum related to multiplication and division of decimal numbers, introduction and content, real-life situations, use of visual models, and formalization methods of algorithms. As a result of the study, the mathematics curricula related to multiplication and division of decimal numbers includes estimation in Korea and Finland, while Japan and Singapore emphasize real-life connections more, and Finland completes the operations in secondary schools. The introduction and content are intensively provided in a short period of time or distributed in various grades and semesters. The real-life situations are presented in a simple sentence format in all countries, and the use of visual models or formalization of algorithms is linked to the operations of natural numbers in unit conversions. Suggestions were made for textbook development and teacher training programs.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2006.07a
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• pp.319-319
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• 2006

• Journal of the Korean School Mathematics Society
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• v.23 no.2
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• pp.203-222
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• 2020

Because the role of the teacher is important for the education to actualize the goals of the curriculum, the interest about the teacher's knowledges has been addressed as an important research topic. Among them, the pedagogical content knowledge is the knowledge that can emphasize the professionalism of the teacher. In this study, I analyzed the elementary pre-service teachers' the problem solving strategies that they imagined the methods that elementary school students can think about fraction division. Pre-service teachers who participated in this study were completed all of the mathematics education courses in the pre-service teachers' education courses. The research was conducted using the four type-problems of fraction division. The results showed that elementary pre-service teachers responded in the order of equal sharing problem-measurement division-partitive division-context of determination of a unit rate problem. They presented significant responses not only with typical algorithms but also with pictures or expressions. On the basis of this research, we have to take an interest in the necessity of sharing and recognizing various methods of fraction division in pre-service teachers education.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.3
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• pp.185-191
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• 2022

This paper proposed a division algorithm of performance complexity $O{\frac{n(n+1)}{2}}$ for a change-making problem(CMP) in which polynomial time algorithms are not known as NP-hard problem. CMP seeks to minimize the sum of the x_j number of coins exchanged when a given amount of money C is exchanged for c_j,j=1,2,⋯,n coins. Known polynomial algorithms for CMPs are greedy algorithms(GA), divide-and-conquer (DC), and dynamic programming(DP). The optimal solution can be obtained by DP of O(nC), and in general, when given C>2ⁿ, the performance complexity tends to increase exponentially, so it cannot be called a polynomial algorithm. This paper proposes a simple algorithm that calculates quotient by dividing upper triangular matrices and main diagonal for k×n matrices in which only j columns are placed in descending order of c_j of n for c_j ≤ C and i rows are placed k excluding all the dividers in c_j. The application of the proposed algorithm to 39 benchmarking experimental data of various types showed that the optimal solution could be obtained quickly and accurately with only a calculator.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.12C
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• pp.1288-1298
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• 2002

To implement elliptic curve cryptosystem in GF(2$\^$m/) at high speed, a fast divider is required. Although bit-parallel architecture is well suited for high speed division operations, elliptic curve cryptosystem requires large m(at least 163) to support a sufficient security. In other words, since the bit-parallel architecture has an area complexity of 0(m$\^$m/), it is not suited for this application. In this paper, we propose a new serial-in serial-out systolic array for computing division operations in GF(2$\^$m/) using the standard basis representation. Based on a modified version of tile binary extended greatest common divisor algorithm, we obtain a new data dependence graph and design an efficient bit-serial systolic divider. The proposed divider has 0(m) time complexity and 0(m) area complexity. If input data come in continuously, the proposed divider can produce division results at a rate of one per m clock cycles, after an initial delay of 5m-2 cycles. Analysis shows that the proposed divider provides a significant reduction in both chip area and computational delay time compared to previously proposed systolic dividers with the same I/O format. Since the proposed divider can perform division operations at high speed with the reduced chip area, it is well suited for division circuit of elliptic curve cryptosystem. Furthermore, since the proposed architecture does not restrict the choice of irreducible polynomial, and has a unidirectional data flow and regularity, it provides a high flexibility and scalability with respect to the field size m.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.431-455
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• 2013

In this thesis, I classified various meanings of fraction into two categories, i.e concept(rate, operator, division) and model(whole-part, measurement, allotment), and surveyed appearances which is shown in Korea elementary mathematics textbook. Based on this results, I derived several implications on learning-teaching of fraction in elementary education. Firstly, we have to pursuit a unified formation of fraction concept through a complementary advantage of various concepts and models Secondly, by clarifying the time which concepts and models of fraction are imported, we have to overcome a ambiguity or tacit usage of that. Thirdly, the present Korea's textbook need to be improved in usage of measurement model. It must be defined more explicitly and must be used in explanation of multiplication and division algorithm of fraction.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.1-9
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• 2004

The important arithmetic operations over finite fields include exponentiation, division, and inversion. An exponentiation operation can be implemented using a series of squaring and multiplication operations using a binary method, while division and inversion can be performed by the iterative application of an AB$^2$ operation. Hence, it is important to develop a fast algorithm and efficient hardware for this operations. In this paper presents new bit-serial architectures for the simultaneous computation of multiplication and squaring operations, and the computation of an $AB^2$ operation over $GF(2^m)$ generated by an irreducible AOP of degree m. The proposed architectures offer a significant improvement in reducing the hardware complexity compared with previous architectures, and can also be used as a kernel circuit for exponentiation, division, and inversion architectures. Furthermore, since the Proposed architectures include regularity and modularity, they can be easily designed on VLSI hardware and used in IC cards.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.8A
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• pp.1231-1237
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• 2000

DMT기반 VDSL 시스템에서 채널의 주파수 특성에 따라 각 부채널에 각기 다른 비트를 할당하는 "Bit allocation algorithm"은 DMT기반 시스템의 초기화 과정에 필수적으로 사용되며 초기화 시간을 단축하기위해 이알고리즘의 고속화가 필요하다 기존의 알고리즘인 Chow Campello가제시한 알고리즘들은 ADSL과 같이 부채널수가 적은 응용분야에서는 적용 가능했으나 부채널 수가 ADSL의 16배에 이르는 VDSL과 같은 경우에는 계산량이 과다하기 때문에 실시간 적용이 어렵다. 본 논문에서는 수신단에서 계산된 SNR을 미리 계산된 기준 SNR 값과 비교하는 방법을 이용하여 계산량을 줄인 새로운 비트 할당 알고리즘을 제시한다. 제안된 알고리즘은 기존 알고리즘에서 N.log2N의 연산이 필요한 SNR을 내림차순으로 분류하는 과정을 없앴고 log2 연산 덧셈 및 나눗셈의 연산을 단순한 비교 연산으로 대체함으로서 보다 고속으로 각 부채널에 할당할 비트 수를 계산할수 있다 그리고 제안된 고속 알고리즘을 VDSL 시스템에 적용한 결과 기존의 알고리즘인 Chow 알고리즘과 동일한 성능을 보임을 확이하였다.보임을 확이하였다.