• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.125-143
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• 2012

This study is designed to see the characteristics of elementary students' arithmetic error patterns and error rates by going up grades and to draw some implications for effective instruction. For this, 580 elementary students of grade 3-6 are tested with the same subtraction, multiplication and division problems. Their errors are analyzed by the frame of arithmetic error types this study sets. As a result of analysis, it turns out that the children's performance in arithmetic get well as their grades go up and the first learning year of any kind of arithmetic procedures has the largest improvement in arithmetic performance. It is concluded that some arithmetic errors need teachers' caution, but we fortunately find that children's errors are not so seriously systematic and sticky that they can be easily corrected by proper intervention. Finally, several instructional strategies for arithmetic procedures are suggested.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1998.12a
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• pp.537-545
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• 1998

This paper is the research about a joint coding system of source and channel coding using VF(Variable-to-fixed length) arithmetic code and BCH code. We propose a VF arithmetic coding method with EDC( Error Detecting Capability) and a joint coding method in that the VF arithmetic coding method with EDC is combined with BCH code. By combining both the VF arithmetic code with EDC and BCH code. the proposed joint coding method corrects a source codeword with t-errors in decoding of BCH code and carries out a improvement of the EDC of a codeword with more than (t＋1)-errors in decoding of the VF arithmetic coding with EDC. We examine the performance of the proposed method in terms of compression ratio and EDC.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.2
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• pp.428-431
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• 2007

A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.

• School Mathematics
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• v.11 no.4
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• pp.567-581
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• 2009

Many articles have reported that zero causes children's arithmetic errors. This article was designed to measure the effect of zero on children's arithmetic performances. For this, 222 of 3,4,5,6 graders in elementary school were tested with pencil and paper. The test were categorized into four parts: basic number fact, column subtraction, column multiplication, and column division. These data showed that the negative effect of zero on children's arithmetic was limited to several areas, concretely, multiplication facts with zero, column subtraction with numbers which have two successive zeros, column multiplication with numbers which have zero in a middle position, long division with zeros. But there was no evidence that students could self-control these negative effects of zero as grade went up. It implies that we should keep attention to children's arithmetic performance with zero in some special areas.

• JSTS:Journal of Semiconductor Technology and Science
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• v.13 no.5
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• pp.473-481
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• 2013

A fractional folding analog-to-digital converter (ADC) with a novel arithmetic digital encoding technique is discussed. In order to reduce the asymmetry errors of the boundary conditions for the conventional folding ADC, a structure using an odd number of folding blocks and fractional folding rate is proposed. To implement the fractional technique, a new arithmetic digital encoding technique composed of a memory and an adder is described. Further, the coding errors generated by device mismatching and other external factors are minimized, since an iterating offset self-calibration technique is adopted with a digital error correction logic. A prototype 8-bit 1GS/s ADC has been fabricated using an 1.2V 0.13 um 1-poly 6-metal CMOS process. The effective chip area is $2.1mm^2$(ADC core : $1.4mm^2$, calibration engine : $0.7mm^2$), and the power consumption is 88 mW. The measured SNDR is 46.22 dB at the conversion rate of 1 GS/s. Both values of INL and DNL are within 1 LSB.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.169-189
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• 2004

Under the assumption of default priors, such as noninformative priors, Bayesian model determination and parameter estimation of regression models with stationary and invertible ARMA errors are developed under exact full likelihoods. The default Bayes factors, the fractional Bayes factor (FBF) of O'Hagan (1995) and the arithmetic intrinsic Bayes factors (AIBF) of Berger and Pericchi (1996a), are used as tools for the selection of the Bayesian model. Bayesian estimates are obtained by running the Metropolis-Hastings subchain in the Gibbs sampler. Finally, the results of numerical studies, designed to check the performance of the theoretical results discussed here, are presented.

• International Journal of Internet, Broadcasting and Communication
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• v.13 no.3
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• pp.118-123
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• 2021

Recently, digital crime is becoming more intelligent, and efficient digital forensic techniques are required to collect evidence for this. In the case of important files related to crime, a specific person may intentionally delete the file. In such a situation, data recovery is a very important procedure that can prove criminal charges. Although there are various methods to recover deleted files, we focuses on the recovery technique using HxD editor. When recovering a deleted file using the HxD editor, check the file structure and access the file data area through calculation. However, there is a possibility that errors such as arithmetic errors may occur when a file approach through calculation is used. Therefore, in this paper, we propose an algorithm that automatically calculates the header and footer of a file after checking the file signature in the root directory for efficient file recovery. If the algorithm proposed in this paper is used, it is expected that the error rate of arithmetic errors in the file recovery process can be reduced.

• Journal for History of Mathematics
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• v.12 no.1
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• pp.1-12
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• 1999

The first part of this thesis discusses the types and the properties of errors, one of which makes up systematic errors of measurements, removable by detecting their causes, the other errors of accidental causes which can not be removed. The final part of this thesis deals with the historical background of the Gaussian distribution by Hershel, Hagen, Laplace and Gauss from the late 18th century to the early 19th century. It can be concluded that the accidental idea and the treatment of accidental error distribution by Gauss Is the best one based on the assumption that the most probable value of true value is the arithmetic mean of data, obtained by repeated measurements of a given quantity.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.23-47
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• 2017

The purpose of this study is to analyze the types of errors that may occur in the four arithmetic operations of the fractions after classified according to the level of academic achievement for sixth-grade elementary school student who Learning of the four arithmetic operations of the fountain has been completed. The study was proceed to get the information how change teaching content and method in accordance with the level of academic achievement by looking at the types of errors that can occur in the four arithmetic operations of the fractions. The test paper for checking the type of errors caused by calculation of fractional was developed and gave it to students to test. And we saw the result by error rate and correct rate of fraction that is displayed in accordance with the level of academic achievement. We investigated the characteristics of the type of error in the calculation of the arithmetic operations of fractional that is displayed in accordance with the level of academic achievement. First, in the addition of the fractions, all levels of students showing the highest error rate in the calculation error. Specially, error rate in the calculation of different denominator was higher than the error rate in the calculation of same denominator Second, in the subtraction of the fractions, the high level of students have the highest rate in the calculation error and middle and low level of students have the highest rate in the conceptual error. Third, in the multiplication of the fractions, the high and middle level of students have the highest rate in the calculation error and low level of students have the highest rate in the a reciprocal error. Fourth, in the division of the fractions, all levels of students have the highest r rate in the calculation error.

• Structural Engineering and Mechanics
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• v.37 no.6
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• pp.633-648
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• 2011

This paper investigates the aspect-ratio locking of the isoparametric 8-node quadrilateral (QUAD8) element. An important finding is that, if finite element solution is carried out with in exact arithmetic (i.e., with no truncation and round off errors), the locking tendency of the element is completely avoided even for aspect-ratios as high as 100000. The current finite element codes mostly use floating point arithmetic. Thus, they can only avoid this locking for aspect-ratios up to 100 or 1000. A novel method is proposed in the paper to avoid aspect-ratio locking in floating point computations. In this method, the offending terms of the strain-displacement matrix (i.e., $\mathbf{B}$-matrix) are multiplied by suitable scaling factors to avoid ill-conditioning of stiffness matrix. Numerical examples are presented to demonstrate the efficacy of the method. The examples reveal that aspect-ratio locking is avoided even for aspect-ratios as high as 100000.