Showing papers on "Decimal published in 2017"

Hard lessons : Why rational number arithmetic is so difficult for so many people

Abstract: Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of rational number arithmetic: inherent and culturally contingent. Inherent sources of difficulty are ones that are imposed by the task of learning rational number arithmetic, such as complex relations among fraction arithmetic operations. They are present for all learners. Culturally contingent sources of difficulty are ones that vary among cultures, such as teacher understanding of rational numbers. They lead to poorer learning among students in some places rather than others. We conclude by discussing interventions that can improve learning of rational number arithmetic.

Inhibitory control and decimal number comparison in school-aged children.

Abstract: School-aged children erroneously think that 1.45 is larger 1.5 because 45 is larger than 5. Using a negative priming paradigm, we investigated whether the ability to compare the magnitude of decimal numbers in the context in which the smallest number has the greatest number of digits after the decimal point (1.45 vs. 1.5) is rooted in part on the ability to inhibit the "greater the number of digits the greater its magnitude" misconception derived from a property of whole numbers. In Experiment 1, we found a typical negative priming effect with 7th graders requiring more time to compare decimal numbers in which the largest number has the greatest number of digits after the decimal point (1.65 vs. 1.5) after comparing decimal numbers in which the smallest number has the greatest number of digits after the decimal point (1.45 vs. 1.5) than after comparing decimal numbers with the same number of digits after the decimal point (1.5 vs. 1.6). In Experiment 2, we found a negative priming effect when decimal numbers preceded items in which 7th graders had to compare the length of two lines. Taken together our results suggest that the ability to compare decimal numbers in which the smallest number has the greatest number of digits is rooted in part on the ability to inhibit the "greater the number of digits the greater its magnitude" misconception and in part on the ability to inhibit the length of the decimal number per se.

Area Efficient and Fast Combined Binary/Decimal Floating Point Fused Multiply Add Unit

Abstract: In this work we present a new 64-bit floating point Fused Multiply Add (FMA) unit that can perform both binary and decimal addition, multiplication, and fused-multiply-add operations. The presented FMA has 6 percent less delay than the fastest stand-alone decimal unit and 23 percent less area than both binary and decimal units together. These results were achieved by the use of: 1) column by column reduction to reduce the partial products in the multiplier tree, 2) a new leading zeros detector that produces its output in base-3 to simplify the normalization shifting in the binary datapath, 3) the use of a redundant adder to perform the final addition, 4) using a new rounding-while-redundant technique to hide the rounding delay and remove it from the critical path, and 5) using a new simple conversion technique from redundant to binary/decimal.

Conceptual knowledge of decimal arithmetic

Abstract: In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or false: 0.77 * 0.63 > 0.77"), knowledge of decimal magnitudes, and knowledge of decimal arithmetic procedures. Their confidence in their direction of effect judgments was also assessed. The authors found (a) most students incorrectly predicted the direction of effect of multiplication and division with decimals below 1; (b) this pattern held for students who accurately compared the magnitudes of individual decimals and correctly executed decimal arithmetic operations; (c) explanations of direction of effect judgments that cited both the arithmetic operation and the numbers' magnitudes were strongly associated with accurate judgments; and (d) judgments were more accurate when multiplication problems involved a whole number and a decimal below 1 than with 2 decimals below 1. Implications of the findings for instruction are discussed.

High Performance Parallel Decimal Multipliers Using Hybrid BCD Codes

Abstract: A parallel decimal multiplier with improved performance is proposed in this paper by exploiting the properties of three different binary coded decimal (BCD) codes, namely the redundant BCD excess-3 code (XS-3), the overloaded decimal digit set (ODDS) code and the BCD-4221/5211 code The signed-digit radix-10 recoding is used to recode the BCD multiplier to the digit set [-5, 5] from [0, 9] The redundant BCD XS-3 code is adopted to generate the multiplicand multiples in a carry-free manner The XS-3 coded partial products (PPs) are converted to ODDS PPs to fit binary partial product reduction (PPR) In this paper, a regular decimal PPR tree using ODDS and BCD-4221/5211 codes is proposed; it consists of a binary PPR tree block, a non-fixed size BCD-4221 counter block and a BCD-4221/5211 PPR tree block The decimal carry-save algorithm based on BCD-4221/5211 is used in the PPR tree to obtain high performance multipliers Moreover, an improved PPG circuit and an improved parallel prefix/carry-select decimal adder are proposed to further improve the performance of the proposed multipliers Analysis and comparison using the 45 nm technology show that the proposed decimal multipliers are faster and require less hardware area than previous designs found in the technical literature

Uncovering Gender and Problem Difficulty Effects in Learning with an Educational Game

Abstract: A prior study showed that middle school students who used the educational game Decimal Point achieved significantly higher gain scores on immediate and delayed posttests of decimal understanding than students who learned with a more conventional computer-based learning tool. This paper reports on new analyses of the data from that study, providing new insights into the benefits of the game. First, females benefited more than males from the game. Second, students in the game condition performed better on the more difficult intervention problems. This paper presents these new analyses and discusses why the educational game might have led to these results.

Descriptors based unsupervised change detection in satellite images

Abstract: In this paper, a novel unsupervised technique is proposed to get the change analysis of bitemporal satellite images The proposed technique is based on combination of Multi-Block Local Binary Pattern (MB-LBP) descriptor and Binary Robust Independent Elementary Features (BRIEF) descriptor In this approach, the MB-LBP encodes overlapping blocks of both images based on BRIEF encoded decimal values of square sub-regions of considered overlapping block BRIEF generates decimal values by comparing each pixel in each sub-region with a calculated quantity This quantity is generated by taking an average of both center pixel and a calculated threshold To get binary feature vectors for each corresponding pixels of both images, MB-LBP is applied on the obtained decimal values Hamming distance is used as a similarity metric to compare the binary feature vectors of each pixel of both images This provides binary change map of changed and unchanged region Optical satellite images acquired by Landsat satellite are used to perform the experiments Experimental results show that the proposed method provides better results compared to earlier reported techniques like expectation maximization and kernel k-means methods

Optical scheme of conversion of a positionally encoded decimal digit to frequency encoded Boolean form using Mach–Zehnder interferometer-based semiconductor optical amplifier

Abstract: The conversion of decimal number to its equivalent binary one and vice-versa is very important in the field of electronic/optical computing and data processing system. There are so many well established methods for this conversion. In this study, the authors propose a new scheme for optical conversion of a decimal number to its frequency encoded binary equivalent using tree architecture-based system and frequency-encoding principle. To implement the above conversion, some optical non-linear switches, such as Mach–Zehnder interferometer-based semiconductor optical amplifier (SOA), reflecting SOA based on SOA, have been used to get frequency encoded response.

Reproducibility in computational science: a case study: randomness of the digits of pi

Abstract: Mathematical research is undergoing a transformation from a mostly theoretical enterprise to one that involves a significant amount of experimentation. Indeed, computational and experimental mathematics is now a full-fledged discipline with mathematics, and the larger field of computational science is now taking its place as an experimental discipline on a par with traditional experimental fields. In this new realm, reproducibility comes to the forefront as an essential part of the computational research enterprise, and establishing procedures to ensure and facilitate reproducibility is now a central focus of researchers in the field. In this study, we describe our attempts to reproduce the results of a recently published article by Reinhard Ganz, who concluded that the decimal expansion of π is not statistically random, based on an analysis of several trillion decimal digits provided by Yee and Kondo. While we are able to reproduce the specific findings of Ganz, additional statistical analysis le...

Sign-Magnitude Encoding for Efficient VLSI Realization of Decimal Multiplication

Abstract: Decimal $X\times Y$ multiplication is a complex operation, where intermediate partial products (IPPs) are commonly selected from a set of precomputed radix- $10~X$ multiples. Some works require only $[{ 0, 5 }]\times X$ via recoding digits of $Y$ to one-hot representation of signed digits in $ [-5, 5]$ . This reduces the selection logic at the cost of one extra IPP. Two’s complement signed-digit (TCSD) encoding is often used to represent IPPs, where dynamic negation (via one xor per bit of $X$ multiples) is required for the recoded digits of $Y$ in $[-5, -1]$ . In this paper, despite generation of 17 IPPs, for 16-digit operands, we manage to start the partial product reduction (PPR) with 16 IPPs that enhance the VLSI regularity. Moreover, we save 75% of negating xors via representing precomputed multiples by sign-magnitude signed-digit (SMSD) encoding. For the first-level PPR, we devise an efficient adder, with two SMSD input numbers, whose sum is represented with TCSD encoding. Thereafter, multilevel TCSD 2:1 reduction leads to two TCSD accumulated partial products, which collectively undergo a special early initiated conversion scheme to get at the final binary-coded decimal product. As such, a VLSI implementation of $16\times 16$ -digit parallel decimal multiplier is synthesized, where evaluations show some performance improvement over previous relevant designs.

A pulsed decimal technique for single-channel, dynamic signaling for IoT applications

Abstract: Pulsed-Index Communication (PIC) is a recent technique for single-channel communication which is based on the principle of transferring the indices of only the ON bits in the form of a series of pulse streams. In this paper, we present a modified version of PIC which is based on the same underlying idea but with key improvements in data rate and reliability. The proposed technique is called Pulsed Decimal Communication (PDC). Like PIC, PDC is a protocol for single-channel, high-data rate, low-power dynamic signaling that does not require any clock and data recovery. It however achieves higher data rates by introducing a three-step algorithm, comprising a segmentation, an encoding, and a sub-segmentation step. The segmentation step is used to split the data word into smaller segments and therefore smaller decimal numbers to represent them. The encoding step reduces the number of ON bits in the data and relocates them to lower indices. The sub-segmentation step is used to split further the segments into smaller sub-segments. The complete process reduces the number of pulses required to transmit binary data, thus improving the data rate. Compared with PIC, PDC achieves a 78% improvement in data rate and is more reliable as it eliminates the variations in the number of symbols to be transmitted. An FPGA and an ASIC (65nm technology) implementation of the protocol show that the low-power operation and small footprint of PIC are maintained in PDC, which consumes around 25of power at a clock frequency of 25MHz with a gate count of approximately 2150.

Assessment of the Knowledge of the Decimal Number System Exhibited by Students with Down Syndrome

Abstract: This paper presents an assessment of the understanding of the decimal numeral system in students with Down Syndrome (DS). We followed a methodology based on a descriptive case study involving six students with DS. We used a framework of four constructs (counting, grouping, partitioning and numerical relationships) and five levels of thinking for each one. The results of this study indicate the variability of the six students in the five levels and in their mastery of the constructs. The grouping construct, which is essential to a proper development of the others, proved complex for the students. In general, we found that these students have a better procedural than conceptual understanding. However, the skills displayed by two of the students in the study group are encouraging with a view to advancing the number knowledge of these individuals.

Mapping Free Educational Software Intended for the Development of Numerical and Algebraic Reasoning

Abstract: Educational software has significantly changed how mathematics is taught and learned. One challenge for educators is choosing the most appropriate software among numerous options. Therefore, we mapped free mathematics education software according to number and operation content. The study was carried out with public elementary school teachers (grades 6 - 9). The teachers watched a presentation on the features of each software type and filled out a checklist about the software and its content. The results showed that 63% of the 32 software titles were appropriate for developing numeric and algebraic reasoning. According to the teachers, these titles were appropriate for developing and consolidating concepts related to the number system, operations and properties of natural and whole numbers, numeric expressions, divisibility, prime numbers, decomposition into prime factors, GCD, LCM, operations with rational numbers in fraction and decimal form, comparison and operations on equivalent fractions, first degree equations, and first and second degree polynomial functions. https://doi.org/10.26803/ijlter.16.11.3

Integer non-uniform constellation for high-order QAM

Abstract: The present disclosure includes systems and techniques relating to an integer non-uniform constellation (NUC) high-order M-QAM. In some implementations, a scale factor is identified for a mapping of bit patterns into M constellation points of a NUC M-QAM, wherein M is no less than 1024; each of the M constellation points has respective real and imaginary coordinates; and the respective real and imaginary coordinates having respective decimal parts that are integer multiples of 2 −n , with n being a non-negative integer less than 5. A bit pattern is received and mapped to integer real and imaginary coordinates of one of the M constellation points according to a mapping rule of the NUC M-QAM. The integer real and imaginary coordinates of the one of the M constellation points equal the scale factor multiplied with respective real and imaginary coordinates of the one of the M constellation points having respective decimal parts.

Aproximación a la propiedad de densidad del conjunto de los números racionales desde las representaciones en el registro como fracción y el registro decimal

Abstract: In this research we analyze the difficulties of the students of cycle four, specifically the ninth grade, to understand the density property of the set of rational numbers and describe the way in which they attempt to register as a fraction and in the register decimal. Since, in our practice, it encountered serious difficulties for our students to respond to situations involving rational numbers in both the representation register and fraction as in the decimal representation register, Order of Density Property Order Of said numerical set. We constructed a didactic sequence on the study of the density of the rational ones that consists of four sessions in which we collected the information of the difficulties and through a study of three cases, we investigated a depth in the length of the process, the difficulties that the Studied subjects presented and the form of confrontations through the technique of semistructured interviews. It analyzes in each subject the development of the tasks that were worked in the length of the different sessions and in the group of subjects of the categories of analysis in order to how the students of the developed companies, in the way that later they were able to buy The processes intra-subject and the processes between the subjects.

Decimal Dilemmas: Interpreting and Addressing Misconceptions

Abstract: In this article, a student's misconception of multiplication and division of decials is analyzed and findings are presented from preservice teachers’ interpretation of that misconception. The authors then highlight common decimal misconceptions, outline two strategies for addressing such misconceptions in the classroom, and include final remarks connecting the professional noticing framework with addressing misconceptions in mathematics.

Method of displaying tracing points of self-adaptive map scale

Abstract: The invention relates to a method of displaying tracing points of a self-adaptive map scale. Under different map scales, the actual distance of each pixel on the screen is fixed. For each longitude and latitude coordinate, the distance corresponding to each decimal place of longitude and latitude is also fixed. If the maximum distance corresponding to current decimal place of each longitude and latitude is smaller than the actual distance of each decimal place, a fixed decimal place only needs to be retained for each longitude and latitude under a certain map scale, so that more coordinates are repeated and duplicates can be quickly removed. The method provided by the invention can quickly display massive tracing points and keep the shape of the track to the maximum extent, and has the advantages of being high in computing efficiency, keeping the shape of the track and remaining important inflection points and characteristic points, and setting of the initial value is only related to the map scale but is irrelevant to the shape of the track.

The transposition of counting situations in a virtual environment

Abstract: The mathematics education research is increasingly focused on different didactical hypotheses for constructing teaching and learning situations involving the decimal principle of the numeration system. One of these situations is, for example, counting a big collection of objects through the tangible manipulation. In this paper we introduce the simulating device, “Simbuchettes”, for analysing its potential concerning this situation with respect to the tangible material. In particular, we will show that “Simbuchettes” preserves all of the techniques we identified in the tangible world and it allows to mobilise other techniques strongly grounding on the decimal principle of the numeration system that we rarely observed with the tangible material.

A Comparative Analysis of Division in Elementary Mathematics Textbooks in Korea and Japan

Abstract: The purpose of the study is to examine how Korean and Japanese elementary mathematics textbooks series present division in terms of the perspective of making connections. For this purpose, units dealing with division of whole numbers, fractions, and decimal numbers were analyzed with foci on the meanings of division and procedures of division. Findings showed that, in the textbooks of both countries, the various meanings of division were consistently applied not only to whole numbers but also to fractions and decimal numbers. Moreover, the procedures of division were connected as numbers were expanded from whole numbers to fractions. Noticeable differences included: as for the organization of the contents of division, Korean textbooks presented division of fractions first, whereas Japanese textbooks dealt with division of decimal numbers first. Regarding the meanings of division, the Korean textbooks dealt mainly with partition and measurement division situations, while the Japanese counterparts were more inclusive with multiple situations, such as determination of a unit rate. This study is expected to provide information on how Korean and Japanese textbooks present division and to give implications for textbook developers and teachers to connect division meaningfully as students deal with whole numbers, fractions, and decimal numbers.

Information processing apparatus and decimal number conversion method

Abstract: A memory stores conversion data that indicates correspondence between each four-bit string in binary expression and a single digit in decimal expression. A processor selects four consecutive bits out of binary number data and, with reference to the conversion data, determines a value of one digit of decimal number data from a position of the selected four bits in the binary number data and a value of at least part of the selected four bits. The processor then subtracts a binary number corresponding to the determined value of the one digit from the binary number data, thus calculating a difference between them. The processor selects, out of the difference produced by the subtracting, another four consecutive bits located below the previously selected four bits and repeats the above determining to determine another decimal digit so as to convert the binary number data into decimal form.

Using an SN P System to Compute the Product of Any Two Decimal Natural Numbers

Abstract: In this paper, a new SN P system is investigated in order to compute the product of any two decimal natural numbers. Firstly, an SN P system with two input neurons is constructed, which can be used to compute the product of any two binary natural numbers which have specified lengths. Secondly, the correctness of the SN P system is proved theoretically. However, the system can only be used to compute the product of any two binary natural numbers, but the product of any two decimal natural numbers often need to be computed in practical application. Therefore, it is necessary to construct a coding SN P system which converts a decimal number into a binary number and to construct a decoding SN P system which converts a binary number to a decimal number. In the end, an new SN P system is constructed to compute the product of any two decimal natural numbers. An example test shows that the SN P system can be used to compute the product of any two decimal natural numbers. Therefore, this paper provides a new method for constructing the SN P system which can compute the product of any two natural numbers.

A Few Factors from the Euler Product Are Sufficient for Calculating the Zeta Function with High Precision

Abstract: The paper demonstrates by numerical examples a nontraditional way to get high precision values of Riemann’s zeta function inside the critical strip by using the functional equation and the factors from the Euler product corresponding to a very small number of primes. For example, the three initial primes produce more than 50 correct decimal digits of ζ(1/4 + 10i).

The Role of Domain-General Cognitive Abilities and Decimal Labels in At-Risk Fourth-Grade Students' Decimal Magnitude Understanding.

Abstract: The purpose of the study was to determine whether individual differences in at-risk 4th graders' language comprehension, nonverbal reasoning, concept formation, working memory, and use of decimal labels (i.e., place value, point, incorrect place value, incorrect fraction, or whole number) are related to their decimal magnitude understanding. Students (n = 127) completed 6 cognitive assessments, a decimal labeling assessment, and 3 measures of decimal magnitude understanding (i.e., comparing decimals to the fraction 1 2 benchmark task, estimating where decimals belong on a 0–1 number line, and identifying fraction and decimal equivalencies). Each of the domain-general cognitive abilities predicted students' decimal magnitude understanding. Using place value labels was positively correlated with students' decimal magnitude understanding, whereas using whole-number labels was negatively correlated with students' decimal magnitude understanding. Language comprehension, nonverbal reasoning, and concept formation were positively correlated with students' use of place value labels. By contrast, language comprehension and nonverbal reasoning were negatively correlated with students' use of whole number labels. Implications for the development of decimal magnitude understanding and design of effective instruction for at-risk students are discussed.

The Analysis of Students’ Ability of Decimal Numeral Multiplication of the Fifth Grade Students

Abstract: This study aimed to (1) describing Learning multiplication of decimal fractions in V grade,(2) The students' ability in completing the multiplication of decimal fractions, (3) The constraints which were faced by students in completing the multiplication of decimal fractions and the solutions to overcome those obstacles. The type of this study was descriptive quantitative and qualitative research. The subjects of this study were the fifth grade students of SD Negeri 2 Penarukan, consisted of 20 students and teachers in V class. The object of this study were (1) Learning multiplication decimal fraction in V grade, (2) The students' ability in completing the multiplication of decimal fractions, (3) The constraints which were faced by students in completing the multiplication of decimal fractions and the solutions to overcome those obstacles. The observation, test, interview, and documentation were used to collect the data. The data were analyzed using descriptive quantitative and qualitative approach. The results showed (1) Learning multiplication decimal fractions was categorized good with a value of 84 , (2) the average test results in classical 59.9 with low category with the highest indicators is to solve everyday problems which involves multiplication of various fractions 55.25% and the lowest indicator is determining the results of multiplication operations of various fractional 88.5 %, (3) The constraints faced by students are: forget the concept of decimal fractions multiplication operations, forget to put coma at the end of the answer and students are still confusein completing the essay task. The solution to overcome those constraints aregiving students a lot of exercises regarding the multiplication of decimal fractions. So that students are better trained and familiar with the particular multiplication exercises.