Design, Implementation & Performance of Vedic Multiplier Based on Look Ahead Carry Adder for Different Bit Lengths

This paper proposed the layout of Vedic Multiplier based totally on Urdhva Trigbhyam approach of multiplication. It is most effective Vedic sutras for multiplication. Urdhva triyagbhyam is a vertical and crosswise approach to discover product of two numbers. Multiplication is an essential quintessential feature in arithmetic logic operation. Computational overall performance of a DSP device is limited via its multiplication overall performance and since, multiplication dominates the execution time of most DSP algorithms. Multiplication is one of the simple arithmetic operations and it requires extensively extra hardware assets and processing time than addition and subtraction. Our work is to compare different bit Vedic multiplier structure using carry look ahead adder technique. Keywords: Carry Look Ahead Adder, Urdhva Trigbhyam, DSP algorithms, Vedic Multiplier

Step Pyramid Distribution for Prime Numbers

In this document, we will present a new way to visualize the distribution of Prime Numbers in the number system to spot Prime numbers in a subset of numbers using a simpler algorithm. Then we will look throw a classification algorithm to check if a number is prime using only 7 simple arithmetic operations with an algorithm complexity less than or equal to O (7) operations for any number.

A Monolithic Stochastic Computing Architecture for Energy and Area Efficient Arithmetic

As the energy and hardware investments necessary for conventional high-precision digital computing continues to explode in the emerging era of artificial intelligence, deep learning, and Big-data [1-4], a change in paradigm that can trade precision for energy and resource efficiency is being sought for many computing applications. Stochastic computing (SC) is an attractive alternative since unlike digital computers, which require many logic gates and a high transistor volume to perform basic arithmetic operations such as addition, subtraction, multiplication, sorting etc., SC can implement the same using simple logic gates [5, 6]. While it is possible to accelerate SC using traditional silicon complementary metal oxide semiconductor (CMOS) [7, 8] technology, the need for extensive hardware investment to generate stochastic bits (s-bit), the fundamental computing primitive for SC, makes it less attractive. Memristor [9-11] and spin-based devices [12-15] offer natural randomness but depend on hybrid designs involving CMOS peripherals for accelerating SC, which increases area and energy burden. Here we overcome the limitations of existing and emerging technologies and experimentally demonstrate a standalone SC architecture embedded in memory based on two-dimensional (2D) memtransistors. Our monolithic and non-von Neumann SC architecture consumes a miniscule amount of energy < 1 nano Joules for s-bit generation and to perform arithmetic operations and occupy small hardware footprint highlighting the benefits of SC.

A study on multiplication operation on triangular fuzzy numbers

The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.

ANALYZING CONTENT KNOWLEDGE OF PROSPECTIVE ELEMENTARY SCHOOL TEACHERS ON THE MATERIAL OF FRACTIONAL ARITHMETIC OPERATIONS

Teacher quality is one of the most influential factors in student learning. In-depth material knowledge (content) is very important for prospective teachers who will one day become teachers. Thus, analyzing and describing the Content Knowledge (CK) of prospective teachers needs to be done. The purpose of this study is to describe the CK of prospective elementary school teachers (SD/MI) on the material of fractional arithmetic operations. The subjects of this study were three students from Ar-Raniry State Islamic University of Banda Aceh. This research includes qualitative descriptive research, so that the data were analyzed using qualitative data analysis, namely data reduction, data presentation, and drawing conclusions. Data collection in this study was carried out through tests and combined with interviews so that the instruments used were test questions and interview guidelines. The study results indicate that the content knowledge of the three elementary teacher candidates was still weak, there were teacher candidates who did not understand the arithmetic operation hierarchy and still made carelessness in the concept of fractional arithmetic operations.

KEMAMPUAN OPERASI HITUNG BILANGAN BULAT MENGGUNAKAN MEDIA PEMBELAJARAN MANIK-MANIK WARNA

AbstrakTujuan penelitian ini untuk mengetahui: (1) kemampuan operasi hitung bilangan bulat peserta didik kelas VI sebelum menggunakan media pembelajaran manik-manik warna, (2) kemampuan operasi hitung bilangan bulat peserta didik kelas VI setelah menggunakan media pembelajaran manik-manik warna, dan (3) perbedaan kemampuan operasi hitung bilangan bulat pada peserta didik kelas VI SD Negeri 151 Timbula Kec. Bontotiro Kab. Bulukumba sebelum dan setelah menggunakan media pembelajaran manik-manik warna. Penelitian ini merupakan jenis penelitian experimen dengan pre-experimental design. Teknik pengambilan sampel menggunakan sampel jenuh. Sampel dalam penelitian ini yaitu seluruh peserta didik kelas VI SD Negeri 151 Timbula Kec. Bonto Tiro Kab. Bulukumba yang berjumlah 23 orang. Instrumen yang digunakan adalah tes dan dokumentasi. Data yang terkumpul diolah dengan menggunakan analisis statistik deskriptif. Hasil penelitian menunjukkan bahwa: (1) rata-rata nilai kemampuan operasi hitung bilangan bulat peserta didik sebelum diajar menggunakan media pembelajaran manik- manik warna sebesar 29.57, (2) nilai rata-rata setelah diajar menggunakan media manik-manik warna sebesar 77,83, dan (3) terdapat perbedaan kemampuan operasi hitung bilangan bulat pada peserta didik sebelum dan setelah diajar menggunakan media pembelajaran manik-manik warna. Berdasarkan penelitian ini, dapat disimpulkan bahwa penggunaan media pembelajaran manik-manik warna dapat meningkatkan kemampuan operasi hitung bilangan bulat.AbstractThe purpose of this study was to describe: (1) the ability to operate integer counting of class VI students before using color beads learning media, (2) the ability to operate integer counting of class VI students after using the color beads learning media, and (3) the difference in the operating ability of integer counting in class VI of SD 151 Timbula Kec. Bontotiro Kab. Bulukumba before and after using color beads media. The method used was experimental research with a pre-experimental design. The sample was selected using the saturated technique. The sample of this study was all students of class VI of SD 151Timbula Kec. Bonto Tiro Kab. Bulukumba with a total number of 23 students. The instruments used were tests and documentation. The data analysis technique used was descriptive statistics. The results showed that: (1) the average value of the integer count operation ability of students before being taught using the color beads learning media was 29.57, (2) the average value after being taught using color beads media was 77.83, and (3) there were differences in the ability to operate integer count operations of students before and after being taught using color. From this study, it could be concluded that the use of color beads learning media could improve the ability of integer arithmetic operations.

A Comparative Study of Homomorphic Encryption Schemes Using Microsoft SEAL

Fully homomorphic encryption (FHE) technology is a method of encrypting data that allows arbitrary calculations to be computed. Machine learning (ML) and many other applications are relevant to FHE such as Cloud Computing, Secure Multi-Party, and Data Aggregation. Only the authenticated user has the authority to decrypt the ciphertext and understand its meaning, as encrypted data can be computed and processed to produce an encrypted output. Homomorphic encryption uses arithmetic circuits that focus on addition and multiplication, allowing the user to add and multiply integers while encrypted. This paper discusses the performance of the Brakerski-Fan-Vercauteren scheme (BFV) and Cheon, Kim, Kim, and Song (CKKS) scheme using one of the most important libraries of FHE “Microsoft SEAL”, by applying certain arithmetic operations and observing the time consumed for every function applied in each scheme and the noise budget after every operation. The results obtained show the difference between the two schemes when applying the same operation and the number of sequential operations each can handle.

Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.