• Journal of the Korea Society of Computer and Information
• /
• v.4 no.4
• /
• pp.94-100
• /
• 1999

This paper concerns the implementation of a digital neural network which performs the high speed operation of Hopfield model's arithmetic operation. It is also designed to use a look-up table and produce floating point arithmetic of nonlinear function with high speed operation. The arithmetic processing of Hopfleld is able to describe the matrix-vector operation, which is adaptable to design the array processor because of its recursive and iterative operation .The proposed method is expected to be applied to the field of real neural networks because of the realization of the current VLSI techniques.

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 1991.10a
• /
• pp.86-91
• /
• 1991

A capability of performing the optical logic and arithmetic operations is followed by an effective encoding technique. In this paper, we proposed the color light encoding technique. By using this encoding technique, the space bandwidth product(SBP) is minimized in the output plane. In addition, we proposed the pre-operation pro-carry processing method that performs faster than the same time operation and carry processing method in optical computing. We proposed that the color liquid crystal device(CLCD) is used as the encoded color light input source.

• The Mathematical Education
• /
• v.40 no.2
• /
• pp.335-343
• /
• 2001

Algebra is important part of mathematics education. Recent days, many mathematics educators emphasize on real world situation. Form real situation, pupils make sense of concepts, and mathematize it by reflective thinking. After that they formalize the concepts in abstract. For example, operation in numbers develops these course. Operation in natural number is an arithmetic, but operation on real number is algebra. Transition from arithmetic to algebra has the cutting point in representing the concepts to mathematics sign system. In this note, we see the cognitive tendency of 10th grade about operation of real number, their cutting point of transition from arithmetic to algebra, and show some methods of helping pupils.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.27 no.6
• /
• pp.910-920
• /
• 1990

This paper presents a method of constructing an Arithmetic Operation Unit Systems (A.O.U.S.) over Galois Field GF(2**m) for the purpose of the four arithmetical operation(addition, subtraction, multiplication and division between two elements in GF(2**mm). The proposed A.O.U.S. is constructed by following procedure. First of all, we obtained each four arithmetical operation algorithms for performing the four arithmetical operations using by mathematical properties over GF(2**m). Next, for the purpose of realizing the four arithmetical unit module (adder module, subtracter module, multiplier module and divider module), we constructed basic cells using the four arithmetical operation algorithms. Then, we realized the four Arithmetical Operation Unit Modules(A.O.U.M.) using basic cells and we constructd distributor modules for the purpose of merging A.O.U.M. with distributor modules. Finally, we constructed the A.O.U.S. over GF(2**m) by synthesizing A.O.U.M. with distributor modules. We prospect that we are able to construct an Arithmetic & Logical Operation Unit Systems (A.L.O.U.S.) if we will merge the proposed A.O.U.S. in this paper with Logical Operation Unit Systems (L.O.U.S.).

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.36C no.8
• /
• pp.35-45
• /
• 1999

In this paper, the addition and the multiplicative algorithm of two polynomials over finite field $GF(p^m)$ are presented. The 4-valued arithmetic processor of the serial input-parallel output modular structure on $GF(4^3)$ to be performed the presented algorithm is implemented by current mode CMOS. This 4-valued arithmetic processor using current mode CMOS is implemented one addition/multiplication selection circuit and three operation circuits; mod(4) multiplicative operation circuit, MOD operation circuit made by two mod(4) addition operation circuits, and primitive irreducible polynomial operation circuit to be performing same operation as mod(4) multiplicative operation circuit. These operation circuits are simulated under $2{\mu}m$ CMOS standard technology, $15{\mu}A$ unit current, and 3.3V VDD voltage using PSpice. The simulation results have shown the satisfying current characteristics. The presented 4-valued arithmetic processor using current mode CMOS is simple and regular for wire routing and possesses the property of modularity. Also, it is expansible for the addition and the multiplication of two polynomials on finite field increasing the degree m and suitable for VLSI implementation.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.46 no.12
• /
• pp.66-72
• /
• 2009

This paper proposes an efficient binary arithmetic encoder for CABAC which is used one of the entropy coding methods for H.264/AVC. The present binary arithmetic encoding algorithm requires huge complexity of operation and data dependency of each step, which is difficult to be operated in fast. Therefore, renormalization exploits 2-stage pipeline architecture for efficient process of operation, which reduces huge complexity of operation and data dependency. Context model updater is implemented by using a simple expression instead of transIdxMPS table and merging transIdxLPS and rangeTabLPS tables, which decreases hardware size. Arithmetic calculator consists of regular mode, bypass mode and termination mode for appearance probability of binary value. It can operate in maximum speed. The proposed binary arithmetic encoder has 7282 gate counts in 0.18um standard cell library. And input symbol per cycle is about 1.

• The Journal of Engineering Research
• /
• v.2 no.1
• /
• pp.31-37
• /
• 1997

This paper describes the design and implementation of 8 bit ALU graphic simulator which helps students who study the structure and operation course of general ALU. ALU of this paper consists of three parts, arithmetic circuit, logic circuit, and shifter. Each of them performs as follows. Arithmetic circuit performs arithmetic operation such as addition, subtraction, 1 increment, 1 decrement, 2's complement, logic circuit performs logic operation such as OR, AND, XOR, NOT, and shifter performs shift operation and transfers the result of circuits of arithmetic, logic to data bus. The instructions which relate to these basic ALU functions was selected from Z80 instructions and ALU circuit was designed with those instructions and this designed ALU circuit was implemented on graphic screen. And all state of this data operation course in ALU was showed by bit and logic gate unit.

• East Asian mathematical journal
• /
• v.29 no.4
• /
• pp.355-392
• /
• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• East Asian mathematical journal
• /
• v.38 no.2
• /
• pp.257-275
• /
• 2022

Recently, there are studies the argument that arithmetic rules established by the four fundamental arithmetic operations, in other words, commutative laws, associative laws, distributive laws, should be explicitly described in mathematics textbooks and the curriculum. These rules are currently implicitly presented or omitted from textbooks, but they contain important principles that foster mathematical thinking. This study aims to evaluate the current level of understanding of these computation rules and provide implications for the curriculum and textbook writing. To this end, the correct answer ratio of the five arithmetic rules for 1-4 grades 398 in five elementary schools was investigated and the type of error was analyzed and presented, and the subject to learn these rules and the points to be noted in teaching and learning were also presented. These results will help to clarify the achievement criteria and learning contents of the calculation rules, which were implicitly presented in existing national textbooks, in a new 2022 revised curriculum.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2016.10a
• /
• pp.401-404
• /
• 2016

This paper proposes entropy coding method of HEVC CABAC Encoder for efficient hardware architecture. The Binary Arithmetic Encoder requires data dependency at each step, which is difficult to be operated in a fast. Proposed Binary Arithmetic Encoder is designed 4 stage pipeline to quickly process the input value bin. According to bin approach, either MPS or LPS is selected and the binary arithmetic encoding is performed. Critical path caused by repeated operation is reduced by using the LUT and designed as a shift operation which decreases hardware size and not using memory. The proposed Binary Arithmetic Encoder of CABAC is designed using Verilog-HDL and it was implemented in 65nm technology. Its gate count is 3.17k and operating speed is 1.53GHz.