Effects of shift-left operations on complex binary numbers

Complex numbers play a unique and very important role in many electrical engineering applications. Complex Binary Number System (CBNS) represents a given complex number as a single-unit binary string in contrast to x+iy form of representation using two real values usually represented in IEEE-754 format. Researchers have been exploring various hardware techniques for performing arithmetic operations on CBNS numbers. However, the existing CBNS hardware implementations suffer from the area, speed, and power overheads, with increasing data width. This work proposes an FPGA implementation of a CBNS Co-Processor which consists of an Arithmetic Unit (AU) that can add and subtract (-1+j)-base CBNS numbers of any data width, processing two-bits at a time. The proposed CBNS Co-Processor architecture is implemented on various FGPA platforms and verified its functionality. The proposed CBNS Co-Processor executes addition and subtraction operations 2.36 and 3.22 times faster respectively compared to the existing CBNS adder and subtractor implementations.

We introduce a novel method for complex number representation. The proposed, redundant complex binary number system (RCBNS) is developed by combining a redundant binary number and a complex number in base (-1+j). Donald (1960) and Walter Penny (1964, 1965) represented complex numbers using base -j and (-1+j) in the classified algorithmic models. A redundant complex binary number system consists of both real and imaginary-radix number systems that form a redundant integer digit set. This system is formed by using complex radix of (-1+j) and a digit set of /spl alpha/=3, where /spl alpha/ assumes a value of -3, -2, -1, 0, 1, 2, 3. The arithmetic operations of complex numbers with this system treat the real and imaginary parts as one unit. The carry-free addition has the advantage of redundancy in number representation in the arithmetic operations. Results of the arithmetic operations are in the RCBNS form. The two methods for conversion from the RCBNS form to the standard binary number form have been presented. The RCBNS reduces the number of steps required to perform complex number arithmetic operations, thus enhancing the speed.

A number system uses a set of digits and sign to represent all the numbers. Different number systems use different amount of digits and sign. To compare the leanness of a number system, the cardinality of the complete set of digits and sign are employed in this work. The 01 binary number system is used by almost all the modern computers. It can represent all the real numbers by two digits 0, 1 and a sign (-), which means its cardinality is 3. Thus, the 01 binary system is not a true binary system. After reviewing all the existing number systems it is found that no true binary system exists for real numbers. All the current binary number systems either don’t have radix 2, or have cardinality 3. In this paper, a true binary system for real numbers, with both radix and cardinality 2, is invented based on the principle of Yin-Yang. Surprisingly, this binary system can not only represent all real numbers without using a sign, but also perform arithmetic and Boolean operations without any problem. Furthermore, due to its radix being 2, this true binary system is compatible with the 01 binary system and many operations are interchangeable between the two systems. It is expected that this true binary system will be applied in the fields of number representation, computer science and cryptography.

The article describes the book of the Italian mathematician Francesco Brunetti "Arimmetica binomica...", published in 1746. Examples of numbers from the book, examples of addition, subtraction, multiplication, division and extraction of the square root in the binary system, as well as binary values of the logarithms of a number of numbers are given. The book also presents operations on fractions and mixed binary numbers. Attention is drawn to the original way of writing binary numbers proposed by Brunetti. According to this method, instead of the entire binary number, only the numbers (in the form of decimal digits) of those digits in which units are represented (with numbering starting from the right) are recorded. Ordinal numbers of digits greater than 9, Brunetti proposes to designate as their last digit (0, 1, ..., 9), writing a comma (prime) to the right of all such digits, and numbers greater than 19 — similarly with two commas, etc. With such a notation, four arithmetic operations on binary numbers are greatly facilitated (the article provides an example of adding the numbers written accordingly).

Computer operations involving complex numbers, essential in such applications as digital signal processing and image processing, are usually performed in a divide-and-conquer approach dealing separately with the real and imaginary parts and then accumulating the results. There have been several proposals to treat complex numbers as a single unit but all seem to have floundered on the basic problem of the division process without which, of course, it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single binary representation and provides a fail-safe procedure for obtaining the quotient of two complex numbers expressed in this representation.

For many years, vector space models have been used in information retrieval and computational linguistics to represent terms, queries, and documents, using vector addition as a simple operator to model semantic composition. Though surprisingly successful, many aspects of meaning including word order, typed relationships, and nested structures are not captured by this modelling process.

У статті пропонується до розгляду концепція розробки інформаційно-керуючих систем на основі біноміальних систем числення, в основі якої лежить нова інформаційна технологія обробки даних на базі біноміальних чисел. В рамках даної технології проводиться формування кодових об'єктів біноміальної структури, їх перетворення в двійкові біноміальні числа і зворотне перетворення результуючих кодових об'єктів у вихідні дані на основі двійкової системи числення. Наведені підходи до вирішення типових інформаційних задач з використанням біноміальних чисел.

It is shown that metals and alloy binary systems are widely used in technology due to the uniqueness of their mechanical, physical and chemical properties. Anisotropy of mechanical and electrical properties, which is due to cold plastic deformation, is not unimportant. Binary systems use is not limited to the mechanical engineering industry but also finds application in electrical engineering, automobile, aircraft, and rocket production. In this case, many parts are obtained by metal forming methods, which are characterized by ultimate plastic strain, heating, and hardening. Therefore, to predict the quality of products made of bimetallic compositions, it is necessary to be able to control the stress and deformation fields in the form alteration process. This is achieved by analyzing the component's initial mechanical properties, threshold deformation, anisotropy, hardness, and plasticity, and electrical conductivity. Based on this information, it is possible to find the system deformation regularities in which there is an inextricable layer connection. It is shown that as a result of the binary system deformation, the soft layer deformation becomes more difficult, and the hard layer deformation is facilitated, which leads to the convergence of the soft and hard layers deformation, and, consequently, to a decrease in the uneven bimetal deformation. This circumstance affects the electrical resistance of the bimetal and leads to anisotropy of electrical conductivity, which consequently contributes to an increase in heat losses due to eddy currents in electrical grids and devices.

Modern digital communication systems rely heavily on baseband signal processing for in-phase and quadrature (I-Q) channels, and complex number processing in low-voltage CMOS has become a necessity for channel equalization, timing recovery, modulation, and demodulation. In this work, redundant binary (RB) arithmetic is applied to complex number multiplication for the first time so that an N-bit parallel complex number multiplier can be reduced to two RE multiplications (i.e., an addition of N RB partial products) corresponding to real and imaginary parts, respectively. This efficient RE encoding scheme proposed can generate RB partial products with no additional hardware and delay overheads. A prototype 8-bit complex number multiplier containing 11.5 K transistors is integrated on 1.05/spl times/1.33 mm/sup 2/ using 0.8 /spl mu/m CMOS. The chip consumes 90 mW with 2.5 V supply when clocked at 200 MHz.

Guest Editorial

Before the era of the high-speed electronic digital computers the representation of numbers in the decimal numerical form was exclusively used in computational practice. The design of the first program-controlled mathematical machines (for instance, Harvard Mark I and ENIAC) was also based on the decimal number system. It took long time before the merit of other polyadic form (for instance, the dyadic or binary number system) was recognized for this purpose. Compatibility with the switching properties of electronic elements and simplicity of logic are outstanding features claimed for the use of the binary system. The algorithms for the arithmetic operations in computing machines can also be based on a numerical system which is not polyadic, i. e. on the numerical System of Residual Classes (SRC). The SRC-encoding of numbers in computers has certain unexpected theoretical as well as practical features. To begin with, the theoretical background of SRC number representation and characteristics of SRC arithmetic operations and algorithms are presented in this paper in form of a condensed survey appended by some elucidating examples. The question of encoding of numbers to be transmitted through the data channels and processed in the SRC arithmetic unit is considered to be of predominant importance as to its practical applicability. There are two basic methods of encoding which are known and which have already been used at advantage to design computing circuits: the one-out-of-n code to represent n integers by n bits and the combinatory code of representing 2 n integers by n bits. The SRC permits to develop another system of encoding which is, in fact, a combination of the two methods of encoding mentioned above. Logical circuits for arithmetic operations based on this type of coding have certain interesting features which are discussed in the paper. The author is aware of the fact that his effort to present a clear and unified picture of the SRC is certainly far from being satisfactory. The SRC is only, in its first stages of evolution, influenced by practical applications in computing machines. New conceptions, algorithms and logical circuits can be expected for the future.

GIS, geographic information systems, software is a set of computer programs allows storage, retrieval, analysis and display of spatial data which may reveal hidden patterns and assists smart decision - making. Recently, GIS systems have been used in Electrical Engineering applications such as to find out the best location to build an electrical engineering generating station, decide about an electrical distribution network or to establish a line- of- sight cellular telecommunication network. In addition many other GIS applications in electrical engineering are becoming feasible. We are proposing a GIS course for senior electrical engineering students, which will allow the electrical engineering students to be introduced to GIS and its possible applications in electrical engineering. Currently most of the electric authorities world wide use GIS in their daily business, therefore such a course will open new opportunities to the EE graduates and also shorten training period if a graduate joins a GIS operation or an electric authority. The course will be 3 credit hours for one semester, two hours theoretical and one hour practical .

ABSTRACTArtificial intelligence (AI) is increasingly recognized as a vital tool in electrical engineering, offering automation, error reduction, and enhanced accessibility. However, its adoption has lagged compared to other fields, highlighting a need for a comprehensive examination of its applications and challenges. This study systematically reviews AI applications in electrical engineering, classifying research findings to uncover progress, challenges, and opportunities. It aims to identify trends, gaps, and implications to guide future research and practical applications. A systematic literature review (SLR) was conducted, analyzing studies published between 2014 and 2024. Fifty‐seven publications meeting inclusion criteria were categorized into five themes: AI algorithms, power engineering, smart grid technologies, electric vehicle systems, and AI integration. The review revealed growing interest in AI applications within electrical engineering, with a significant rise in publications, particularly from China. AI algorithms demonstrated broad applicability and versatility across various domains, highlighting their potential for innovation. Additionally, there is a considerable opportunity for developing and applying frameworks to test AI innovations in electrical engineering. AI integration in electrical engineering has advanced significantly in areas such as power engineering, smart grid technologies, and electric vehicle systems. However, substantial untapped potential remains, particularly in developing frameworks for testing AI innovations. This review underscores the importance of global research efforts and identifies promising directions for advancing AI applications in electrical engineering research and practice.

Algorithms are developed to compute the number of active devices for residue number system (RNS) and binary number system (BNS) signal processing architectures. The precharged CMOS technology is used in order to build the filter architecture. The ROM lookup table and two's complement multiplier are used as the computational cells in the RNS and BNS, respectively. A direct implementation transversal systolic filter architecture is considered in RNS and BNS algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modern low-coercivity thermomagnetic materials used in electrical engineering, electronics, and tool engineering are reviewed. They are primarily for the manufacture of magnetic shunts, magnetic secondary resistances, and temperature-sensitive elements for relays, whose response time is determined by the temperature near the Curie point). The effect of alloying additives (Mo, Cr, Cu) on the magnetic properties, heat treatment, and properties of structural changes in iron–nickel alloys is considered. The advantages of new thermomagnetic powder materials in comparison with cast alloys are demonstrated. Also, the prospects of their application in electrical engineering are considered.