Automatic addition

1963 ◽  
Vol 10 (3) ◽  
pp. 127-132
Author(s):  
Franz E. Hohn
Keyword(s):  
Magnetic Tape ◽  
Number System ◽  
Magnetic Core ◽  
The Other ◽  
Binary Number ◽  
Magnetic Cores ◽  
Related Machines

Computers and related machines employ devices such as switches, electron tubes, transistors, magnetic cores, magnetic tape, and so on to do their work of storing, processing, and computing numbers. Since a switch is either open or closed, a tube or transistor is either conducting electricity or not conducting electricity, and a magnetic core or a spot on a magnetic tape is magnetized either “positively” or “negatively,” that is, since one of two opposite conditions is always present, it is natural that the internal operation of such machines should be based on the binary number system, which counts by twos. One of the two conditions is used to represent the number 1, the other to represent the number 0.

scholarly journals Application of Mathematics in Computer Science

2021 ◽  
pp. 339-344
Author(s):  
Dr. Dhiraj Yadav
Keyword(s):  
Artificial Intelligence ◽  
Computer Science ◽  
Number System ◽  
The Other ◽  
Discrete Mathematics ◽  
Binary Number ◽  
Analytical Skills ◽  
New Concepts ◽  
The Subject ◽  
The Universe

No one escape the learning of mathematics in one way or other, ranging from our kitchen to our journey from earth to Moon or Mars. Mathematics persists everywhere around us. It can be perceived in our garden or park from symmetry of leaves, flowers, fruits etc. and by so many examples of Geometry and symmetry can be seen in nature. God used mathematics in creation of the universe in one form or the other. Likewise, Mathematics is the queen of all sciences. Scientists and researchers can not perfectly accomplish their work without including mathematics. Mathematics is the foundation of Computer Science. If one is eager to learn any arena of Computer Science, first he/she has to imbibe a love of Mathematics that will be supportive for progressive learning of the said subject. Mathematics is friendly for analytical skills needed in Computer Science. Concepts of binary number system, Boolean algebra, Calculus, Discrete mathematics, linear algebra, number theory, and graph theory are the most applicable to the subject of computer science with the emergence of new concepts like machine learning, artificial intelligence, virtual reality and augmented reality.

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.

Efficient reversible quantum design of sig-magnitude to two's complement converters

2020 ◽  
Vol 20 (9&10) ◽  
pp. 747-765
Author(s):  
F. Orts ◽  
G. Ortega ◽  
E.M. E.M. Garzon
Keyword(s):  
Quantum Computing ◽  
Scientific Community ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
State Of The Art ◽  
The Other ◽  
Quantum Computers ◽  
Binary Number ◽  
Quantum Cost ◽  
The One

Despite the great interest that the scientific community has in quantum computing, the scarcity and high cost of resources prevent to advance in this field. Specifically, qubits are very expensive to build, causing the few available quantum computers are tremendously limited in their number of qubits and delaying their progress. This work presents new reversible circuits that optimize the necessary resources for the conversion of a sign binary number into two's complement of N digits. The benefits of our work are two: on the one hand, the proposed two's complement converters are fault tolerant circuits and also are more efficient in terms of resources (essentially, quantum cost, number of qubits, and T-count) than the described in the literature. On the other hand, valuable information about available converters and, what is more, quantum adders, is summarized in tables for interested researchers. The converters have been measured using robust metrics and have been compared with the state-of-the-art circuits. The code to build them in a real quantum computer is given.

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

scholarly journals Image Detection System for Schmidt Plates

1984 ◽  
Vol 78 ◽  
pp. 169-171 ◽  
Author(s):  
Hideo Maehara ◽  
Tomohiko Yamagata
Keyword(s):  
Magnetic Tape ◽  
Detection System ◽  
Automated Detection ◽  
The Other ◽  
Image Detection ◽  
Alternative Method ◽  
Intermediate Medium

A 14-inch Schmidt plate contains 109 photographic grains and 105 to 106 images of stars and galaxies on it. Such a quantity of data is too large to be handled in a conventional way even for a big computer.There is, in general, an alternative method to solve this problem; one is to store the data of all pixels on intermediate medium (e.g., magnetic tape), and reduce them into image parameters afterwards. The other method is to do all the processing simultaneously with the measurement. The latter is very useful for the automated detection of celestial images on large Schmidt plates.

scholarly journals Revisiting Sum of Residues Modular Multiplication

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Yinan Kong ◽  
Braden Phillips
Keyword(s):  
Public Key Cryptography ◽  
Number System ◽  
Residue Number System ◽  
The Other ◽  
Public Key ◽  
Modular Multiplication ◽  
Residue Number ◽  
The Cost

In the 1980s, when the introduction of public key cryptography spurred interest in modular multiplication, many implementations performed modular multiplication using a sum of residues. As the field matured, sum of residues modular multiplication lost favor to the extent that all recent surveys have either overlooked it or incorporated it within a larger class of reduction algorithms. In this paper, we present a new taxonomy of modular multiplication algorithms. We include sum of residues as one of four classes and argue why it should be considered different to the other, now more common, algorithms. We then apply techniques developed for other algorithms to reinvigorate sum of residues modular multiplication. We compare FPGA implementations of modular multiplication up to 24 bits wide. The sum of residues multipliers demonstrate reduced latency at nearly 50% compared to Montgomery architectures at the cost of nearly doubled circuit area. The new multipliers are useful for systems based on the Residue Number System (RNS).

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