Design of ALU and Code Converter Using Matrix Calculation
Nirina Gilbert Rasolofoson,
Raoelina Andriambololona
Issue:
Volume 6, Issue 3, June 2017
Pages:
89-100
Received:
3 April 2017
Accepted:
15 April 2017
Published:
27 May 2017
Abstract: Arithmetic Logic Unit (ALU) is a fundamental building block of a central processing unit (CPU) in any computing system. The ALU is the hardware that performs logical (and, or, xor) and basic arithmetic (addition, subtraction, multiplication, division) operations. Thus, its construction requires techniques in which the treatment of operands should be consistent with operations rules. In this paper, ALU based on matrix calculation introduced and developed by Raoelina Andriambololona is proposed. These techniques aim to remove illogic and inconsistent appearing in the international writing numeration with the usual rules in arithmetic. We also propose the design of code converters which convert Binary to BCD (Binary Coded Decimal) code and vice versa using matrix calculation.
Abstract: Arithmetic Logic Unit (ALU) is a fundamental building block of a central processing unit (CPU) in any computing system. The ALU is the hardware that performs logical (and, or, xor) and basic arithmetic (addition, subtraction, multiplication, division) operations. Thus, its construction requires techniques in which the treatment of operands should b...
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Remarks on A-skew-adjoint, A-almost Similarity Equivalence and Other Operators in Hilbert Space
Isaiah Nalianya Sitati,
Bernard Nzimbi,
Stephen Luketero,
Jairus Khalagai
Issue:
Volume 6, Issue 3, June 2017
Pages:
101-107
Received:
28 April 2017
Accepted:
9 May 2017
Published:
29 June 2017
Abstract: In this paper, notions of A-almost similarity and the Lie algebra of A-skew-adjoint operators in Hilbert space are introduced. In this context, A is a self-adjoint and an invertible operator. It is shown that A-almost similarity is an equivalence relation. Conditions under which A-almost similarity implies similarity are outlined and in which case their spectra is located. Conditions under which an A-skew adjoint operator reduces to a skew adjoint operator are also given. By relaxing some conditions on normal and unitary operators, new results on A -normal, binormal and A-binormal operators are proved. Finally A-skew adjoint operators are characterized and the relationship between A-self- adjoint and A-skew adjoint operators is given.
Abstract: In this paper, notions of A-almost similarity and the Lie algebra of A-skew-adjoint operators in Hilbert space are introduced. In this context, A is a self-adjoint and an invertible operator. It is shown that A-almost similarity is an equivalence relation. Conditions under which A-almost similarity implies similarity are outlined and in which case ...
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