A novel method for arithmetic operations using complex binary number system and the reconversion of the result to the decimal complex number system

2004 ◽  
Author(s):  
H. Zaini ◽  
R.G. Deshmukh
Keyword(s):  
Complex Number ◽  
Number System ◽  
Binary Number ◽  
Arithmetic Operations ◽  
Novel Method

scholarly journals Towards Formulation of a Complex Binary Number System

2002 ◽  
Vol 7 (1) ◽  
pp. 199
Author(s):  
Tariq Jamil ◽  
David Blest ◽  
Amer Al-Habsi
Keyword(s):  
Complex Number ◽  
Computer Arithmetic ◽  
Number System ◽  
Divide And Conquer ◽  
Complex Numbers ◽  
Binary Number ◽  
Computer Engineering ◽  
Real Numbers ◽  
Arithmetic Operations ◽  
The Individual

For years complex numbers have been treated as distant relatives of real numbers despite their widespread applications in the fields of electrical and computer engineering. These days computer operations involving complex numbers are most commonly performed by applying divide-and-conquer technique whereby each complex number is separated into its real and imaginary parts, operations are carried out on each group of real and imaginary components, and then the final result of the operation is obtained by accumulating the individual results of the real and imaginary components. This technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a complex number as one unit and to carry out all operations in this form. In this paper, we have analyzed and proposed a (–1–j)-base binary number system for complex numbers. We have discussed the arithmetic operations of two such binary numbers and outlined work which is currently underway in this area of computer arithmetic.  

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

Application of Arithmetic Operations Method in Single Pair-Pole Magnetic Encoder

2011 ◽  
Vol 128-129 ◽  
pp. 85-91
Author(s):  
Yi Fan Zeng ◽  
Rui Li
Keyword(s):  
High Speed ◽  
Angle Measurement ◽  
Single Pair ◽  
Nonlinear Correction ◽  
Arithmetic Operations ◽  
Rotational Angle ◽  
Voltage Signal ◽  
Fpga Chip ◽  
Novel Method ◽  
Hall Sensors

This paper proposes a novel method called arithmetic operations to analyze and process the generated voltage-signal from the single pair-pole magnetic encoder. Dual orthogonal voltage-signals are generated by two vertical hall sensors which are placed in the bottom of a columned magnet. When signals pass A/D converter, the quadrant determination, arithmetic operations and nonlinear correction in FPGA chip are performed before the values of rotational angle are displayed on the LED. This paper also designs and implements the single pair-pole magnetic encoder which has advantages such as high-speed, high-resolution and high-accuracy in the area of angle measurement.

scholarly journals Step Pyramid Distribution for Prime Numbers

2022 ◽  
Vol 14 (1) ◽  
pp. 55
Author(s):  
Shaimaa said soltan
Keyword(s):  
Number System ◽  
Prime Numbers ◽  
Classification Algorithm ◽  
Algorithm Complexity ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
Simpler Algorithm

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.

Complex Binary Number System-based Co-Processor Design for Signal Processing Applications

2021 ◽  
Author(s):  
Sudia Sai Santosh ◽  
Tandyala Sai Swaroop ◽  
Tangudu Kavya ◽  
Ramesh Chinthala
Keyword(s):  
Signal Processing ◽  
Number System ◽  
Binary Number ◽  
Processor Design

Decimal Hardware Multiplier

2018 ◽  
pp. 4607-4618
Author(s):  
Mário Pereira Vestias
Keyword(s):  
Number System ◽  
Floating Point ◽  
Binary Number ◽  
Correct Result ◽  
Fundamental Operation ◽  
Floating Point Arithmetic ◽  
Decimal Arithmetic ◽  
Decimal Numbers ◽  
Decimal Multiplication ◽  
Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal Multiplication is a fundamental operation utilized in many algorithms and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This article focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

Decimal Hardware Multiplier

2019 ◽  
pp. 722-736
Author(s):  
Mário Pereira Vestias
Keyword(s):  
Number System ◽  
Floating Point ◽  
Binary Number ◽  
Correct Result ◽  
Fundamental Operation ◽  
Floating Point Arithmetic ◽  
Decimal Arithmetic ◽  
Decimal Numbers ◽  
Decimal Multiplication ◽  
Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating-point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal multiplication is a fundamental operation utilized in many algorithms, and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This chapter focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

scholarly journals Algorithm for obtaining palindromes of the binary number system

2020 ◽  
Vol 1679 ◽  
pp. 032069
Author(s):  
V V Lyubimov ◽  
R V Melikdzhanyan
Keyword(s):  
Number System ◽  
Binary Number

Review: Arithmetic as Mathematics

1993 ◽  
Vol 24 (2) ◽  
pp. 172-176
Author(s):  
Vicky L. Kouba
Keyword(s):  
Complex Number ◽  
Mathematics Teaching ◽  
Number System ◽  
Whole Numbers ◽  
The Past ◽  
Children’S Learning ◽  
Flexible Knowledge ◽  
Children's Learning

Too often in the past “arithmetic” has been viewed as simple computing or simple acquisition of procedures. In contrast, the chapters in Analysis of Arithmetic for Mathematics Teaching portray arithmetic as a thoughtful building of a flexible knowledge of our complex number system, rich in concepts, connections, and patterns that are crucial for understanding most of the rest of mathematics. This book provides research foundations and conceptual analyses of the standard topics of arithmetic: understanding of and operations on whole numbers, fractions, and decimals. The authors provide updates on the results, theories, and thoughts about children's learning of arithmetic concepts and processes, a field that has coalesced over the past twenty years.

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