Redundant Radix-2r Number System for Accelerating Arithmetic Operations on the FPGAs

2008 ◽  
Author(s):  
Kensuke Kawakami ◽  
Koji Shigemoto ◽  
Koji Nakano
Keyword(s):  
Number System ◽  
Arithmetic Operations

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.

2. The laws of algebra

2015 ◽  
pp. 11-24
Author(s):  
Peter M. Higgins
Keyword(s):  
Number System ◽  
Arithmetic Operations ◽  
Distributive Law ◽  
Associative Law

‘The laws of algebra’ explores the three laws that govern arithmetic operations and explains how these rules are extended so that they continue to be respected as we pass from one number system to a greater one that subsumes the former. The associative law of addition shows that that (a + b) + c = a + (b + c), and the associative law of multiplication is a(bc) = (ab)c. The distributive law tells us how to multiply out the brackets: a(b + c) = ab + ac. The commutative law of addition is a + b = b + a, a law that holds equally well for multiplication: ab = ba.

The Approximate Number System (ANS) and Discriminating Magnitudes

2020 ◽  
pp. 127-139
Author(s):  
Ellen Peters
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
Math Ability ◽  
Intuitive Sense

This chapter, “The Approximate Number System (ANS) and Discriminating Magnitudes,” discusses our intuitive, rather than deliberative, understanding of numbers. Humans are born with an innate sense of number and an ability to perform simple arithmetic operations with sets of objects without counting. We share this intuitive sense of numeric magnitude (how big one quantity is relative to another) with other species. Non-human animals cannot count as humans do. However, they have a keen sense of quantity that allows them to tell quickly and efficiently which quantity is bigger so that they can make better choices about food, mates, and safety. In humans, this intuitive sense of numbers develops from infancy to adulthood, and it appears to underlie the emergence of symbolic math ability (objective numeracy) in children.

Helping English-Language Learners Develop Computational Fluency

2003 ◽  
Vol 9 (6) ◽  
pp. 294-299 ◽  
Author(s):  
Rusty Bresser
Keyword(s):  
English Language Learners ◽  
Language Learners ◽  
English Language ◽  
Number System ◽  
Arithmetic Operations ◽  
Computational Fluency ◽  
Mathematical Ideas ◽  
Solution Strategies

Students who are computationally fluent can solve problems accurately, efficiently, and with flexibility. These students draw on a repertoire of strategies when solving problems, and their choice of strategies often depends on the type of problem they are solving and the numbers involved. Computational fluency is rooted in an understanding of arithmetic operations, the base-ten number system, and number relationships. Communicating mathematical ideas is fundamental to developing computational fluency. When students share their solution strategies with others, they learn that there are many ways to solve problems and that some strategies are more efficient than others.

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.  

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