scholarly journals On The Implementation of Densely Packed Decimal Number System Based Adder: Prospects and Challenges

2021 ◽  
Vol 25 (1) ◽  
pp. 20-30
Author(s):  
Srikant Kumar Beura ◽  
◽  
Rekib Uddin Ahmed ◽  
Bishnulatpam Pushpa Devi ◽  
Prabir Saha ◽  
...  
Keyword(s):  
Circuit Simulation ◽  
Number System ◽  
Decimal Digit ◽  
Performance Parameters ◽  
Design Technique ◽  
Digit Number ◽  
Time Saving ◽  
Decimal Number ◽  
Decimal Adder ◽  
Pros And Cons

Decimal digit number computation, through bit compression methodology, offers space and time saving, which can be incurred by the Chen-Ho and Densely Packed Decimal (DPD) coding techniques. Such coding techniques have a property of bit compression, like, three decimal digits can be represented by 10 bits instead of 12 bits in binary coded decimal (BCD) format. The compression has been obtained through the elimination of the redundant 0’s from BCD representation. This manuscript reports the pros and cons of the techniques mentioned above. The logic level functionalities have been examined through MATLAB, whereas circuit simulation has been erified through Cadence Spectre. Performance parameters (such as delay, power consumption) have been evaluated through CMOS gpdk45 nm technology. Furthermore, the best design has been chosen from them, and the decimal adder design technique has been incorporated in this paper.

“Pick-a-word”—a base-26 generalization of “Pica-Centro”

1974 ◽  
Vol 21 (5) ◽  
pp. 401-403
Author(s):  
Srisakdi (Sak) Charmonman ◽  
Deborah K. Reed
Keyword(s):  
Number System ◽  
Digit Number ◽  
Decimal Number

The games of Pico-Fumi (Gessel et al. 1972) and Pica-Centro (Aichele 1972) a re number games in the decimal number system. The objective of the games is to logically deduce an n-digit number where n equals two in Pico-Fumi and three in Pica-Centro. An extension to larger numbers of digits was suggested in Douglas Aichele's article, but a more challenging and useful generalization will be proposed here.

scholarly journals Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 518
Author(s):  
Natividad Adamuz-Povedano ◽  
Elvira Fernández-Ahumada ◽  
M. Teresa García-Pérez ◽  
Jesús Montejo-Gámez
Keyword(s):  
Teaching And Learning ◽  
Number Sense ◽  
Methodological Approach ◽  
Number System ◽  
Algebraic Thinking ◽  
First Year ◽  
Symbolic Language ◽  
Decimal Number ◽  
Language Characteristic ◽  
Theoretical Foundations

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

scholarly journals Genetic code as an image of the mirror image. Supplement 1

2019 ◽  
Author(s):  
Miloje M. Rakočević
Keyword(s):  
Amino Acids ◽  
Genetic Code ◽  
Binary Tree ◽  
Mirror Symmetry ◽  
Essential Feature ◽  
Binary Sequence ◽  
Number System ◽  
Mirror Image ◽  
Chemical Similarity ◽  
Decimal Number

Searching for the answer to the question why – in the generating of the genetic code – only mirror symmetrical left and not right amino acids (AAs) were selected, in a previous work we showed the existence of a double Boolean "triangle" in mirror symmetry, with superposition of the top vertices: 00 -11-22 / 22-11-00 → 00-11-22-11-00 [0 as 000; 1 as 001; 2 as 010] (Rakočević, 2019a). The resulting sequence, summed with the binary sequence of a 6-bit binary tree, split with a mirror in the middle (101/010) [as in Dirac's positron / electron mirror], results in a sequence of decimal number system: 02-13-24-16-05, where a smaller number (010 = 2) was added three times and a larger number (101 = 5) twice (Survey 1). The mirror image of the obtained decimal sequence (20-31-42-61-50) is 100% consistent with the arrangement of protein AAs, arranged according to strict chemical similarity (Rakočević, 2019a, Table 3). Starting from this result, the paper of which this is a supplement, presents new insights and new examples of mirror symmetry valid for the genetic code, showing that mirror symmetry is also in other respects an essential feature of the genetic code. In this Supplement are given the further new insights.

scholarly journals Squaring Technique using Vedic Mathematics

2021 ◽  
Author(s):  
Jasmine Bajaj ◽  
Babita Jajodia
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Number System ◽  
Approximation Technique ◽  
Approximation Techniques ◽  
Vedic Mathematics ◽  
Decimal Number ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
Interesting Approach

Vedic Mathematics provides an interesting approach to modern computing applications by offering an edge of time and space complexities over conventional techniques. Vedic Mathematics consists of sixteen sutras and thirteen sub-sutras, to calculate problems revolving around arithmetic, algebra, geometry, calculus and conics. These sutras are specific to the decimal number system, but this can be easily applied to binary computations. This paper presented an optimised squaring technique using Karatsuba-Ofman Algorithm, and without the use of Duplex property for reduced algorithmic complexity. This work also attempts Taylor Series approximation of basic trigonometric and inverse trigonometric series. The advantage of this proposed power series approximation technique is that it provides a lower absolute mean error difference in comparison to previously existing approximation techniques.

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

2017 ◽  
Vol 6 (1) ◽  
pp. 56 ◽  
Author(s):  
Aurelia Noda ◽  
Alicia Bruno
Keyword(s):  
Down Syndrome ◽  
Conceptual Understanding ◽  
Number System ◽  
Study Group ◽  
Descriptive Case Study ◽  
Decimal Number ◽  
Number Knowledge

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.

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