Arithmetic Operations: Addition and Subtraction

2006 ◽  
pp. 55-80
Keyword(s):  
Arithmetic Operations ◽  
Addition And Subtraction

Parallel-sequential adder-subtractor with the highest digits forward on neurons

2021 ◽  
Author(s):  
S.S. Shevelev
Keyword(s):  
Computer System ◽  
Control Unit ◽  
Arithmetic Operations ◽  
Mathematical Functions ◽  
Simple Arithmetic ◽  
Addition And Subtraction

The article deals with the development of a parallel-sequential adder-subtractor that performs arithmetic operations of addition and subtraction of binary numbers in the format with a fixed comma with the highest digits forward. The result of performing arithmetic operations is the sum and difference of binary numbers in the direct code of eight digits. The sum and difference of numbers is calculated on neuropositive elements, the transfer to the highest digits when summing and the loan from the highest digits when subtracting is determined by the majority elements. The algorithm for adding numbers in direct codes allows you to get the result in direct code. The signed digits of numbers determine which operation should be performed on numbers using the sum modulo two operation. If the characters are the same, the result will be zero. Otherwise, the result will be one. After that, the addition or subtraction operation is selected. Summation is performed if the numbers have the same signs, the result is assigned the sign of the first number. Subtraction is performed if the numbers have different signs, the result is assigned the sign of a larger modulo number. The adder-subtracter senior digits forward on neurons contains: block input, block comparatii, the block parallel-serial addersubtracter, the unit registers a larger number, the unit of determining the transfer and loan, a unit registers a smaller number of unit registers a result, the control unit, majority, threshold and neural elements. The device can be used as an arithmetic co-processor in a computer system. It significantly speeds up calculations of both simple arithmetic operations and results of various mathematical functions.

scholarly journals Parsing Algebraic Word Problems into Equations

2015 ◽  
Vol 3 ◽  
pp. 585-597 ◽  
Author(s):  
Rik Koncel-Kedziorski ◽  
Hannaneh Hajishirzi ◽  
Ashish Sabharwal ◽  
Oren Etzioni ◽  
Siena Dumas Ang
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Word Problems ◽  
Single Equation ◽  
Manual Annotation ◽  
Arithmetic Operations ◽  
Discriminative Models ◽  
Small Set ◽  
Addition And Subtraction

This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as Alges.We compare Alges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, Alges overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.

Performing Balanced Ternary Logic and Arithmetic Operations with Spiking Neural P Systems with Anti-Spikes

2012 ◽  
Vol 505 ◽  
pp. 378-385 ◽  
Author(s):  
Xian Wu Peng ◽  
Xiao Ping Fan ◽  
Jian Xun Liu
Keyword(s):  
Logic Gates ◽  
P Systems ◽  
P System ◽  
Ternary Logic ◽  
Arithmetic Operations ◽  
Spiking Neural P Systems ◽  
Addition And Subtraction ◽  
Distributed And Parallel Computing ◽  
Computing Models ◽  
Natural Way

Spiking neural P systems are a class of distributed and parallel computing models inspired by P systems and spiking neural networks.Spiking neural P system with anti-spikes can encode the balanced ternary three digits in a natural way using three states called anti-spikes, no-input and spikes. In this paper we use this variant of SN P system to simulate universal balanced ternary logic gates including AND,OR and NOT gate and to perform some basic balanced ternary arithmetic operations like addition and subtraction on balanced ternary integers. This paper provides an applicational answer to an open problem formulated by L.Pan and Gh. Păun.

scholarly journals Quantum arithmetic operations based on quantum fourier transform on signed integers

2020 ◽  
Vol 18 (06) ◽  
pp. 2050035
Author(s):  
Engin Şahin
Keyword(s):  
Fourier Transform ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Arithmetic Operations ◽  
Absolute Value ◽  
Addition And Subtraction ◽  
Quantum Arithmetic

The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction, division and exponentiation operations are presented. The proposed arithmetic operations can perform nonmodular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two’s complement, absolute value and comparison operations are also presented by using the proposed QFT-based addition and subtraction operations.

scholarly journals The differential relationship between finger gnosis, and addition and subtraction: An fMRI study

2018 ◽  
Vol 3 (3) ◽  
pp. 694-715 ◽  
Author(s):  
Firat Soylu ◽  
David Raymond ◽  
Arianna Gutierrez ◽  
Sharlene D. Newman
Keyword(s):  
Numerical Cognition ◽  
Third Graders ◽  
Arithmetic Operations ◽  
Fmri Study ◽  
Left And Right ◽  
Addition And Subtraction ◽  
Fact Retrieval ◽  
The Impact ◽  
The Relationship ◽  
Differential Relationship

The impact of fingers on numerical cognition has received a great deal of attention recently. One sub-set of these studies focus on the relation between finger gnosis (also called finger sense or finger gnosia), the ability to identify and individuate fingers, and mathematical development. Studies in this subdomain have reported mixed findings so far. While some studies reported that finger gnosis correlates with or predicts mathematics abilities in younger children, others failed to replicate these results. The current study explores the relationship between finger gnosis and two arithmetic operations—addition and subtraction. Twenty-four second to third graders participated in this fMRI study. Finger sense scores were negatively correlated with brain activation measured during both addition and subtraction. Three clusters, in the left fusiform, and left and right precuneus were found to negatively correlate with finger gnosis both during addition and subtraction. Activation in a cluster in the left inferior parietal lobule (IPL) was found to negatively correlate with finger gnosis only for addition, even though this cluster was active both during addition and subtraction. These results suggest that the arithmetic fact retrieval may be linked to finger gnosis at the neural level, both for addition and subtraction, even when behavioral correlations are not observed. However, the nature of this link may be different for addition compared to subtraction, given that left IPL activation correlated with finger gnosis only for addition. Together the results reported appear to support the hypothesis that fingers provide a scaffold for arithmetic competency for both arithmetic operations.

Device for Calculating Logical and Arithmetic Operations

2021 ◽  
Vol 12 (7) ◽  
pp. 350-357
Author(s):  
S. S. Shevelev ◽  
Keyword(s):  
Fixed Point ◽  
High Speed ◽  
High Performance ◽  
Arithmetic Operations ◽  
Structural Scheme ◽  
Computing Systems ◽  
Logical Operations ◽  
Addition And Subtraction

A device has been developed that performs logical and arithmetic operations, which can be used to create high-performance, high-speed computing systems. Specialized blocks perform logical operations: AND, OR, NOT, arith­metic operations: addition and subtraction of binary numbers. Arithmetic operations are performed in direct fixed-point codes. The device is presented in the form of a structural scheme, structural and functional schemes of blocks and an algorithm for the operation of the device.

The addition and subtraction of quantum matrix based on GNEQR

2019 ◽  
Vol 17 (07) ◽  
pp. 1950056
Author(s):  
Hai-Sheng Li ◽  
Yusi Xu ◽  
Yunbai Qin ◽  
Deli Fu ◽  
Hai-Ying Xia
Keyword(s):  
Simulation Experiment ◽  
Quantum Algorithms ◽  
Simulation Method ◽  
Quantum Circuits ◽  
The Novel ◽  
Arithmetic Operations ◽  
Matrix Operations ◽  
Addition And Subtraction ◽  
Quantum Matrix ◽  
First Time

The efficient quantum circuits of arithmetic operations are important to perform quantum algorithms. To implement efficient matrix operations, we first modify the generalized model of the novel enhanced quantum representation of digital images (GNEQR) to store unsigned and signed integer matrices. Next, we design the circuits of the circuits of quantum addition, quantum modulo addition, quantum subtraction, and quantum modulo subtraction, these operations all keeping two operands unchanged. Then, we propose the circuits of quantum matrix addition, quantum matrix modulo addition, quantum matrix subtraction, and quantum matrix modulo subtraction for the first time. Furthermore, we present a simulation method to verify the correctness of the proposed arithmetic operations of matrix. The results of simulation experiment show that the propose arithmetic operations of matrix are efficient and correct.

scholarly journals A Complete Arithmetic Calculator Constructed from Spiking Neural P Systems and its Application to Information Fusion

2020 ◽  
Vol 31 (01) ◽  
pp. 2050055 ◽  
Author(s):  
Gexiang Zhang ◽  
Haina Rong ◽  
Prithwineel Paul ◽  
Yangyang He ◽  
Ferrante Neri ◽  
...  
Keyword(s):  
Information Fusion ◽  
Arithmetic Operation ◽  
P Systems ◽  
Arithmetic Operations ◽  
Spiking Neural P Systems ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Basic Probability ◽  
Addition And Subtraction

Several variants of spiking neural P systems (SNPS) have been presented in the literature to perform arithmetic operations. However, each of these variants was designed only for one specific arithmetic operation. In this paper, a complete arithmetic calculator implemented by SNPS is proposed. An application of the proposed calculator to information fusion is also proposed. The information fusion is implemented by integrating the following three elements: (1) an addition and subtraction SNPS already reported in the literature; (2) a modified multiplication and division SNPS; (3) a novel storage SNPS, i.e. a method based on SNPS is introduced to calculate basic probability assignment of an event. This is the first attempt to apply arithmetic operation SNPS to fuse multiple information. The effectiveness of the presented general arithmetic SNPS calculator is verified by means of several examples.

scholarly journals Peningkatan Kemampuan Operasi Hitung Penjumlahan dan Pengurangan Dengan Media Konkret Pada Siswa Kelas 1 SD Negeri Bantarkawung 03

2020 ◽  
Vol 3 (4) ◽  
pp. 556
Author(s):  
Alif Rizkiana
Keyword(s):  
Elementary School ◽  
Action Research ◽  
Elementary School Students ◽  
First Grade ◽  
Arithmetic Operations ◽  
School Students ◽  
Concrete Objects ◽  
Quality Of Learning ◽  
Addition And Subtraction

<em>The arithmetic operations of addition and subtraction are basic mathematics that must be learned since the 1st grade of elementary school to make it easier for students to do mathematics in advanced grades. In this research, the aim is to improve the ability to do arithmetic operations of addition and subtraction with concrete media for grade 1 students at SD Negeri Bantarkawung 03. Through classroom action research, the quality of learning can be improved because the teacher immediately knows what needs to be improved. The number of respondents studied in this study were all first grade elementary school students, totaling 22 students. This research was carried out in 2 cycles. Based on the description of the implementation of the action, the results of the research and discussion, data were obtained that there was an increase in the ability to do arithmetic addition and subtraction operations in each cycle. It can be seen from the application of the pre-cycle, that is, 40% has increased to 20%, so the total is 60% in the first cycle, then it has increased in the second cycle, which is an increase of 27%, the total increase is 87%. The conclusion is that using concrete objects media can improve the ability of addition and subtraction arithmetic operations in grade 1 students of SD Negeri Bantarkawung 03</em>

scholarly journals SPECIFICS OF TEACHING THE INVERSE RELATIONS BETWEEN THE ARITHMETIC OPERATIONS ADDITION AND SUBTRACTION DURING THE EDUCATION IN MATHEMATICS IN GRADE 1

2021 ◽  
Vol 2 ◽  
pp. 331-337
Author(s):  
Maria Temnikova
Keyword(s):  
Primary School ◽  
Mathematical Knowledge ◽  
First Graders ◽  
Research Work ◽  
Mathematical Tasks ◽  
Arithmetic Operations ◽  
Theoretical Concepts ◽  
Level Of Knowledge ◽  
Addition And Subtraction ◽  
The Republic

One of the fundamental knowledge in mathematics in Primary school is related to the arithmetic operations addition and subtraction. According to the educational programs in mathematics in the Republic of Bulgaria, students start studying these operations in grade 1. The article presents theoretical concepts affecting studying the arithmetic operations addition and subtraction in the education in mathematics at a primary school. The research work identified the specifics of studying the inverse connections between the arithmetic operations addition and subtraction in the education in mathematics for grade 1 are also presented. Some of the significant tasks with importance for discovering the relations between the forward operation addition and the reverse operation subtraction were proposed in the study. A new methodology system of work with tasks where these relations are used was developed and tested. The author studied the knowledge, skills, and competencies of the grade 1 students to solve arithmetic operations addition and subtraction tasks. After the exit diagnostic, it was found out that the students of the class where the new methodology system of work was applied during their education in mathematics have got a higher level of knowledge and skills from competency Cluster Numbers in respect of the arithmetic operations addition and subtraction.  The use of mathematical tasks with reverse relations between the arithmetic operations addition and subtraction help the students to develop both the overall mathematical knowledge and the logical thinking of the first-graders.

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