• The Mathematical Education
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• v.57 no.3
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• pp.311-328
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• 2018

In school mathematics, the concept of an average is not a concept that is limited to a unit of statistics. In particular, high school students will learn about arithmetic mean and geometric mean in the process of learning absolute inequality. In calculus learning, the concept of average is involved when learning the concept of average speed. The arithmetic mean is the same as the procedure used when students mean the test scores. However, the procedure for obtaining the geometric mean differs from the procedure for the arithmetic mean. In addition, if the arithmetic mean and the geometric mean are the discrete quantity, then the mean rate of change or the average speed is different in that it considers continuous quantities. The average concept that students learn in school mathematics differs in the quantitative nature of procedures and objects. Nevertheless, it is not uncommon to find out how students construct various mathematical concepts into mathematical knowledge. This study focuses on this point and conducted the interviews of the students(three) in the second grade of high school. And the expression of students in the process of average concept formation in arithmetic mean, geometric mean, average speed. This study can be meaningful because it suggests practical examples to students about the assertion that various scholars should experience various properties possessed by the average. It is also meaningful that students are able to think about how to construct the mean conceptual properties inherent in terms such as geometric mean and mean speed in arithmetic mean concept through interview data.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.12
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• pp.2921-2926
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• 2013

In this paper, a decimal floating-point arithmetic unit(DFP) was proposed and redesigned to support high speed arithmetic operation employed parallel processing technique. The basic architecture of the proposed DFP was based on the L.K.Wang's DFP and improved it enabling high speed operation by parallel processing for two operands with same size of exponent. The proposed DFP was synthesized as a target device of xc2vp30-7ff896 using Xilinx ISE and verified by simulation using Flowrian tool of System Centroid co. Compared to L.K.Wang's DFP and reference [6]'s method, the proposed DFP improved data processing speed about 8.4% and 3% respectively in case of same input data.

• Journal for History of Mathematics
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• v.12 no.2
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• pp.47-54
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• 1999

We introduce some historical facts on number theory, especially prime numbers and modular arithmetic. And then, with the viewpoint of computer arithmetic, residue number systems are considered as an alternate to positional number systems so that high performance and high speed computation can be achieved in a specified domain such as cryptography and digital signal processing.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.636-639
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• 2004

In present, there are many methods such as DCT, Wavelet Transform, or Quantization -to the image compression field, but the basic image compression method have based on DCT. The representative thing of the efficient techniques for information compression is DCT method. It is more superior than other information conversion method. It is widely applied in digital signal processing field and MPEG and JPEG which are selected as basis algorithm for an image compression by the international standardization group. It is general that DCT is consisted of using multiplier with main arithmetic blocks having many arithmetic amounts. But, the use of multiplier requires many areas when hardware is embodied, and there is fault that the processing speed is low. In this paper, we designed the hardware module that could run high-speed operation using row-column separation calculation method and Chen algorithm by distributed arithmetic method using ROM table instead of multiplier for design DCT module of high speed.

• ETRI Journal
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• v.30 no.5
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• pp.707-717
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• 2008

This paper presents two types of high-speed hardware architectures for the block cipher ARIA. First, the loop architectures for feedback modes are presented. Area-throughput trade-offs are evaluated depending on the S-box implementation by using look-up tables or combinational logic which involves composite field arithmetic. The sub-pipelined architectures for non-feedback modes are also described. With loop unrolling, inner and outer round pipelining techniques, and S-box implementation using composite field arithmetic over $GF(2^4)^2$, throughputs of 16 Gbps to 43 Gbps are achievable in a 0.25 ${\mu}m$ CMOS technology. This is the first sub-pipelined architecture of ARIA for high throughput to date.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.4
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• pp.774-780
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• 2017

This paper proposes an efficient binary arithmetic encoder hardware architecture for CABAC encoding, which is an entropy coding method of HEVC. CABAC is an entropy coding method that is used in HEVC standard. Entropy coding removes statistical redundancy and supports a high compression ratio of images. However, the binary arithmetic encoder causes a delay in real time processing and parallel processing is difficult because of the high dependency between data. The operation of the proposed CABAC BAE hardware structure is to separate the renormalization and process the conventional iterative algorithm in parallel. The new scheme was designed as a four-stage pipeline structure that can reduce critical path optimally. The proposed CABAC BAE hardware architecture was designed with Verilog HDL and implemented in 65nm technology. Its gate count is 8.07K and maximum operating speed of 769MHz. It processes the four bin per clock cycle. Maximum processing speed increased by 26% from existing hardware architectures.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1125-1128
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• 1998

A new architecture for high-speed implementation of adaptive decision-feedback equalizer (ADFE) applicable to wide-band digital wireless modems is described. Rather than using conventional two's complement arithmetic, a novel complex-valued filter structure is devised, which is based on redundant binary (RB) arithmetic. The proposed RB complex-valued filter reduces the critical path delay of ADFE, as well as leads to a more compact implementation than conventional methods. Also, the carry-propagation free (CPF) operation of the RB arithmetic enhances its speed. To demonstrate the proposed method, a prototype chip set is designed. They are designed to contain two complexvalued filter taps along with their coefficient updating circuits, and can be cascaded to implement loger filter taps for high bit-rate applications.

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

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.5
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• pp.1345-1359
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• 1996

This paper presents a floating point arithmetic unit (FPAU) for supescalar microprocessor that executes fifteen operations such as addition, subtraction, data format converting, and compare operation using two pipelined arithmetic paths and new rounding and normalization scheme. By using two pipelined arithmetic paths, each aritchmetic operation can be assigned into appropriate arithmetic path which high speed operation is possible. The proposed normalization an rouding scheme enables the FPAU to execute roundig operation in parallel with normalization and to reduce timing delay of post-normalization. And by predicting leading one position of results using input operands, leading one detection(LOD) operation to normalize results in the conventional arithmetic unit can be eliminated. Because the FPAU can execuate fifteen single-precision or double-precision floating-point arithmetic operations through three-stage pipelined datapath and support IEEE standard 754, it has appropriate structure which can be ingegrated into superscalar microprocessor.