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Designing a Boolean Algebra Tool and Its Use in the Classroom

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Conference

2012 ASEE Annual Conference & Exposition

Location

San Antonio, Texas

Publication Date

June 10, 2012

Start Date

June 10, 2012

End Date

June 13, 2012

ISSN

2153-5965

Conference Session

CoED General Technical Session II

Tagged Division

Computers in Education

Page Count

13

Page Numbers

25.406.1 - 25.406.13

Permanent URL

https://peer.asee.org/21164

Download Count

15

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Paper Authors

biography

Howard Whitston University of South Alabama

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Howard Ernest Whitston is an Instructor at the University of South Alabama, School of Computing, having taught at several colleges and universities since 1983. He has two B.S. degrees, one in mathematics and one in chemistry. He has two M.S. degrees, one in biochemistry, the other one in CIS, specializing in Computer Science. He has been at the University of South Alabama since 2005. Whitston is a member of ACM (Association for Computing Machinery), ACS (American Chemical Society), IEEE-Computer Society, MAA (Mathematical Association of America), and ASEE (since Dec. 2011).

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biography

Adam Thomas Moore University of South Alabama

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Adam Moore is a computer science and mathematics major at the University of South Alabama. He is interested in artificial intelligence and bioinformatics.

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Abstract

Designing a Boolean Algebra Tool and its use in the Classroom Computer Science (CS) students who take a course in Digital Logic during the secondyear of the CS curriculum study Boolean Algebra and its relationship to combinational logiccircuit description. A study of the "Boolean Theorems," which are rules that define the behaviorof Boolean Algebra operators, is part of this coursework. These rules, in theory, can be used toalgebraically simplify the equation of a circuit, which usually leads to a smaller circuit that willcost less to produce. A solid understanding of Boolean Algebra concepts is likewise needed tounderstand the more complicated aspects of combinational logic circuits. Additionally, studentstaking college-level mathematics and philosophy courses typically study Boolean Algebra. Normally in this class, the textbook shows a few, easy to simplify Boolean expressionsand implies that, in general, it is a matter of changing the order of the terms or adding the rightterm or application of one theorem that allows the student to reduce the complex expression intoone containing fewer operators and symbols. Problems usually contain hints as to how to changethe given expression into a simpler one using the “easy to verify” Boolean Theorems, not theones that aren’t intuitive. An interactive program that displays the steps in the simplification of Boolean Algebraexpressions would aid in the students' understanding. The Object-Oriented-Programming (OOP)paradigm can be used to implement such a program. A well-designed class hierarchy canrepresent the parts of a Boolean Algebra expression. These include Symbols, AND expressions,and OR expressions. Classes representing these parts are organized in a sub-class hierarchy. A properly organized hierarchy allows for the Boolean Theorems to be expressed usingthe principles of inheritance and operator overloading. A common convention in Boolean Algebrais using the '+' and '*' signs to represent OR and AND, respectively. The interactions betweenBoolean objects are centered around specifying how each object should behave as an operand ofthese operators. The use of this tool in its final form would allow the students to explore the BooleanAlgebra expression simplification by having the program show which theorems are being used ateach step of the reduction. Testing and assessment of this program in its current state by studentsand areas of possible improvement will be discussed. Future work in the project includes rigorous testing, verification of complex expressionsimplification, and adding a GUI for displaying results.

Whitston, H., & Moore, A. T. (2012, June), Designing a Boolean Algebra Tool and Its Use in the Classroom Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. https://peer.asee.org/21164

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