• IEMEK Journal of Embedded Systems and Applications
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• v.11 no.4
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• pp.227-233
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• 2016

Efficient finite field arithmetic is essential for fast implementation of error correcting codes and cryptographic applications. Among the arithmetic operations over finite fields, the multiplication is one of the basic arithmetic operations. Therefore an efficient design of a finite field multiplier is required. In this paper, two new bit-parallel systolic multipliers for $GF(2^m)$ fields defined by AOP(all-one polynomial) have proposed. The proposed multipliers have a little bit greater space complexity but save at least 22% area complexity and 13% area-time (AT) complexity as compared to the existing multipliers using AOP. As compared to related works, we have shown that our multipliers have lower area-time complexity, cell delay, and latency. So, we expect that our multipliers are well suited to VLSI implementation.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.311-320
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• 2015

In 1613 the official-scholar LI Zhi-zao (李之藻) of the Ming Dynasty, in collaboration with the Italian Jesuit Matteo RICCI (利瑪竇), compiled the treatise Tongwen Suanzhi (同文算指). This is the first book which transmitted into China in a systematic and comprehensive way the art of written calculation that had been in common practice in Europe since the sixteenth century. This paper tries to see what pedagogical lessons can be gleaned from the book, in particular on the basic operations in arithmetic and related applications in various types of problems which form the content of modern day mathematics in elementary school education.

• Korean Journal of Child Studies
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• v.27 no.1
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• pp.139-151
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• 2006

This study was conducted to examine the effects of mathematical activities with online mathematical contents on children's arithmetic development and attitudes toward mathematical activities. Pre- and post-tests were administered to 62 5-year-old children. Differences of children's arithmetic development level and attitudes toward mathematical activities were found between the experimental group using online mathematical contents and the control group using offline mathematical contents. All findings proved that online mathematical contents were effective and had positive influences on children's arithmetic development and attitudes toward mathematical activities. This supports the proposition that online mathematical contents can provide an important means to the improvement of children's mathematical development and attitudes toward mathematical activities.

• 한국데이터정보과학회:학술대회논문집
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• 2006.11a
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• pp.81-95
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• 2006

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

• Journal of the Korea Computer Industry Society
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• v.3 no.2
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• pp.149-158
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• 2002

This paper deals with design and verification of an arithmetic logic unit(ALU) to be used for development of optical computers. The ALU is based on optical switching device, $LiNbO_3$, which is easy to interface with electronic technology and most common in the market. It consists of an arithmetic/logic circuit performing logic operations, memory devices storing operands and the results of operations, and supplementary circuits to select instruction codes, and operates in bit-serial manner. In addition, a simulator is developed for verification of the design, and a set of basic instructions are executed in sequence and step-by-step changes in the accumulator and the memory are examined through simulations, to show that various operations are performed correctly.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.170-174
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• 2008

The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, $C_{pk}$. This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, $C_{pk}$ is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the $C_{pk}$ index estimation presented by fuzzy numbers and approximated its membership function using the "min" - norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that $T_w$ (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the $C_{pk}$ index under $T_w-based$ fuzzy arithmetic operations.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.2
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• pp.204-210
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• 1988

The residue number system offers the possibility of high-speed operation and error detection/correction because of the separability of arithmetic operations on each digit. A compact residue arithmetic module named the self-checking pulse-train residue arithmetic circuit is effectively employed as the basic module, and an efficient error detection/correction algorithm in which error detection is performed in each basic module and error correction is performed based on the parallelism of residue arithmetic is also employed. In this case, the error correcting circuit is imposed in series to non-redundant system. This design method has an advantage of compact hardware. Following the proposed method, a 2nd-order recursive fault-tolerant digital filter is practically implemented, and its fault-tolerant ability is proved by noise injection testing.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.571-575
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• 2003

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input--output data using shape preserving operations for least-squares fitting. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using mixed nonlinear program.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.711-714
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• 2005

We propose floating point arithmetic units for geometry operation of mobile 3D graphic processor. The proposed arithmetic units conform to the single precision format of IEEE standard 754-1985 that is a standard of floating point arithmetic. The rounding algorithm applies the nearest toward zero form. The proposed adder/subtraction unit and multiplier have one clock cycle latency, and the inversion unit has three clock cycle latency. We estimate the required numbers of arithmetic operation for Viewing transformation. The first stage of geometry operation is composed with translation, rotation and scaling operation. The translation operation requires three addition and the rotation operation needs three addition and six multiplication. The scaling operation requires three multiplication. The viewing transformation is performed in 15 clock cycles. If the adder and the multiplier have their own in/out ports, the viewing transformation can be done in 9 clock cycles. The error margin of proposed arithmetic units is smaller than $10^{-5}$ that is the request in the OpenGL standard. The proposed arithmetic units carry out operations in 100MHz clock frequency.

• Journal of IKEEE
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• v.17 no.3
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• pp.346-351
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• 2013

Low-cost and low-power are important requirements in mobile systems. Thus, when a floating-point arithmetic unit is needed, 24-bit floating-point format can be more useful than 32-bit floating-point format. However, a 24-bit floating-point arithmetic unit can be risky because it usually has lower accuracy than a 32-bit floating-point arithmetic unit. Consecutive floating-point operations are performed in 3D graphic processors. In this case, the verification of the floating-point operation accuracy is important. Among 3D graphic arithmetic operations, the floating-point division is one of the most difficult operations to satisfy the accuracy of $10^{-5}$ which is the required accuracy in OpenGL ES 3.0. No 24-bit floating-point divider, whose accuracy is algebraically verified, has been reported. In this paper, a 24-bit floating-point divider is analyzed and it is algebraically verified that its accuracy satisfies the OpenGL requirement.