• Communications of Mathematical Education
• /
• v.35 no.4
• /
• pp.505-525
• /
• 2021

In this study, we investigated how multiplication by 2-digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the '×tens' teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.17 no.1
• /
• pp.11-20
• /
• 2007

A fast Montgomery multiplication occupies important to the design of RSA cryptosystem. Montgomery multiplication consists of two addition, which calculates using CSA or RBA. In terms of CSA, the multiplier is implemented using 4-2 CSA o. 5-2 CSA. In terms of RBA, the multiplier is designed based on redundant binary system. In [1], A new redundant binary adder that performs the addition between two binary signed-digit numbers and apply to Montgomery multiplier was proposed. In this paper, we reconstruct the logic structure of the RBA in [1] for reducing time and space complexity. Especially, the proposed RB multiplier has no coupler like the RBA in [1]. And the proposed RB multiplier is suited to binary exponentiation as modified input and output forms. We simulate to the proposed NRBA using gates provided from SAMSUNG STD130 $0.18{\mu}m$ 1.8V CMOS Standard Cell Library. The result is smaller by 18.5%, 6.3% and faster by 25.24%, 14% than 4-2 CSA, existing RBA, respectively. And Especially, the result is smaller by 44.3% and faster by 2.8% than the RBA in [1].

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.16 no.4
• /
• pp.33-41
• /
• 2006

RSA cryptosystem is of great use in systems such as IC card, mobile system, WPKI, electronic cash, SET, SSL and so on. RSA is performed through modular exponentiation. It is well known that the Montgomery multiplier is efficient in general. The critical path delay of the Montgomery multiplier depends on an addition of three operands, the problem that is taken over carry-propagation makes big influence at an efficiency of Montgomery Multiplier. Recently, the use of the Carry Save Adder(CSA) which has no carry propagation has worked McIvor et al. proposed a couple of Montgomery multiplication for an ideal exponentiation, the one and the other are made of 3 steps and 2 steps of CSA respectively. The latter one is more efficient than the first one in terms of the time complexity. In this paper, for faster operation than the latter one we use binary signed-digit(SD) number system which has no carry-propagation. We propose a new redundant binary adder(RBA) that performs the addition between two binary SD numbers and apply to Montgomery multiplier. Instead of the binary SD addition rule using in existing RBAs, we propose a new addition rule. And, we construct and simulate to the proposed adder using gates provided from SAMSUNG STD130 $0.18{\mu}m$ 1.8V CMOS Standard Cell Library. The result is faster by a minimum 12.46% in terms of the time complexity than McIvor's 2 method and existing RBAs.

• Journal of the Ergonomics Society of Korea
• /
• v.14 no.1
• /
• pp.97-104
• /
• 1995

The widespread use of VDU has improved the efficiency of information transmission between man and machine, but has caused new occupational health and ergonomics problems. In this study, we tried to construct a fuzzy hyman performance model of VDU workers in Korea. Fuzzy inferences of human perfor- mance are obtained from the fuzzy inference rule with the job difficulty, CFF, SACL, Type A. and the degree of concentration in VDU work. Eight healthy female undergraduate students at Kyungnam university for subjects aged 20 to 23 years were examined in this experiment. They calculated continuous addition, subtraction, and multiplication of 1 or 2 digit numbers that were produced randomly on the CRT. Subjects peoformed two types of a numeric operation, which easy and difficult work produced 400 and 600 problems within a 40 minute work session, respectively. Subjects were tested over two workdays according to the type of work(easy and difficult) consisting of four 40 minutes work sessions in the morning. Each work lasted for five minutes with a ten minutes rest break. 117 fuzzy inference rules were obtained from the experimental data. The value of consequent part was obtained by a descent method. The difference between real human error and estimated value of fuzzy inference was $1.8075{\pm}1.8591%(M{\pm}SD)$. The difference in easy and diffcult works were $2.69{\pm}2.13%$ and $0.92{\pm}0.93%$, respectively.

• Journal of Elementary Mathematics Education in Korea
• /
• v.19 no.3
• /
• pp.305-321
• /
• 2015

This study started with wondering whether the nonproportional model used in unit assessment for 2nd graders is appropriate or not for them. This study aims to explore the applicability of the nonproportional model to 2nd graders when they learn about numbers. To achieve this goal, we analyzed elementary mathematics textbooks, applied two kinds of tests to 2nd graders who have learned three-digit numbers by using the proportional model, and investigated their cognitive characteristics by interview. The results show that using the nonproportional model in the initial stages of 2nd grade can cause some didactical problems. Firstly, the nonproportional models were presented only in unit assessment without any learning activity with them in the 2nd grade textbook. Secondly, the size of each nonproportional model wasn't written on itself when it was presented. Thirdly, it was the most difficult type of nonproportional models that was introduced in the initial stages related to the nonproportional models. Fourthly, 2nd graders tend to have a great difficulty understanding the relationship of nonproportional models and to recognize the nonproportional model on the basis of the concept of place value. Finally, the question about the relationship between nonproportional models sticks to the context of multiplication, without considering the context of addition which is familiar to the students.