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Transitional Division Algorithms
The Arithmetic Teacher, 1982“Long division is the most difficult process taught in the elementaryschool mathematics program.” During the past decade, this statement has been cited as a justification for poor performance on standardized tests. Could it be that the manner in which the process is developed in the elementary-school program is the culprit, and not the inherent level ...
Robert A. Laing, Ruth Ann Meyer
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IEE Proceedings - Computers and Digital Techniques, 1994
The aim of this paper is to present a unification of constant-division algorithms. Six approaches are reviewed in detail and their relationships are shown by reducing them to equivalent forms. The authors make an extensive analysis of various constant division algorithms and demonstrate their equivalence.
Srinivasan, P., Petry, F. E.
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The aim of this paper is to present a unification of constant-division algorithms. Six approaches are reviewed in detail and their relationships are shown by reducing them to equivalent forms. The authors make an extensive analysis of various constant division algorithms and demonstrate their equivalence.
Srinivasan, P., Petry, F. E.
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Journal of Algebra and Its Applications, 2005
A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero.
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A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero.
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An improvement in the restoring division algorithm (Needy Restoring Division Algorithm)
2009 2nd IEEE International Conference on Computer Science and Information Technology, 2009An improvement in the current restoring computer division algorithm which minimizes the number of restorations performed by the computer. Currently, restoration is checked after each shifting of the register but Needy Restoring Division Algorithm checks restoration only when it is needed.
Nitish Aggarwal +3 more
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Division algorithms and implementations
IEEE Transactions on Computers, 1997Many algorithms have been developed for implementing division in hardware. These algorithms differ in many aspects, including quotient convergence rate, fundamental hardware primitives, and mathematical formulations. The paper presents a taxonomy of division algorithms which classifies the algorithms based upon their hardware implementations and impact
S.F. Obermann, M.J. Flynn
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Digital Arithmetic: Division Algorithms [PDF]
, 2017 Division is one of the basic arithmetic operations supported by every computer system. The operation can be performed and implemented in either hardware or software, or a combination of the two. Although division is not as frequent as addition and multiplication, nowadays most processors implement it in hardware to not compromise the overall ...
MONTUSCHI, PAOLO, Alberto Nannarelli
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Division algorithm and Kronecker’s approximation theorem
The Journal of Analysis, 2020The authors prove the following characterization of irrational numbers: a real number \(\theta\) is irrational, if and only if there exists a sequence \(\{p_n\}\) of integers such that the sequence \(\{||p_n\theta||\}\) is nonconstant for all large \(n\) and \(||p_n\theta||\to 0\).
Gaurav Aggarwal, Jitender Singh
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The Arithmetic Teacher, 1973
A situation problem is an excellent way to get into the development of the division algorithm.
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A situation problem is an excellent way to get into the development of the division algorithm.
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Journal of the Chinese Institute of Engineers, 2001
Abstract This paper describes the design of algorithms for unidirectional division. Rather than the conventional, restoring or nonrestoring, divisions which require both subtraction and addition operations, alternately, during the process of division, the proposed method needs only one direction, either subtraction or addition, but not both, during the
Hao‐Yung Lo +2 more
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Abstract This paper describes the design of algorithms for unidirectional division. Rather than the conventional, restoring or nonrestoring, divisions which require both subtraction and addition operations, alternately, during the process of division, the proposed method needs only one direction, either subtraction or addition, but not both, during the
Hao‐Yung Lo +2 more
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Quantum Division Circuit Based on Restoring Division Algorithm
2011 Eighth International Conference on Information Technology: New Generations, 2011This paper presents a new quantum circuit for implementation of division operation in n-qubit quantum processors based on restoring division algorithm. In the proposed circuit we tried to reduce the number of ancillaqubits as many as possible using quantum fourier transform so that the circuit could be easily generalized for the case of any arbitrary ...
Alireza Khosropour +2 more
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