Boolean Algebra - Welcome to Southern Illinois University
Transcript of Boolean Algebra - Welcome to Southern Illinois University
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Boolean Algebra
Chapter 3
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Boolean ValuesIntroduction
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Boolean OperationsFundamental Operators
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Boolean OperationsBinary Boolean Operators
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Boolean AlgebraPrecedence of Operators
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Boolean AlgebraFunction Evaluation
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Boolean AlgebraBasic Identities
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Boolean AlgebraDuality Principle
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Boolean AlgebraFunction Manipulation (1)
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Boolean AlgebraFunction Manipulation (2)
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Boolean AlgebraFunction Manipulation (3)
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Standard FormsSOP and POS
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Standard FormsMiniterms
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Standard FormsSum of Minterms
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Standard FormsMaxterms
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Standard FormsProduct of Maxterms
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Standard FormsMinterm and Maxterm Exp.
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Standard FormsForming Sum of Minterms
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Standard FormsForming Product of Maxterms
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Standard FormsConverting MIN and MAX
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SimplificationKarnaugh Maps
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SimplificationKarnaugh Map Ordering
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SimplificationImplicants
• ImplicantA product term is an implicant of a function if the function has the value ‘1’ for all minterms of the product term.
• Prime implicantIf the removal of any literal from an implicant P results in a product term that is not an implicant of the function then P is a prime implicant.
• Essential prime implicantA prime implicant that covers a ‘1’ square which is not covered by no other prime implement rectangles.
• Non-essential prime implicantA prime implicant in which all of its covered ‘1’ squares are covered by one or more other prime implicants.
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SimplificationProcedure for SOP
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SimplificationExample for SOP (1)
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SimplificationExample for SOP (2)
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SimplificationProcedure for POS
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SimplificationExample for POS (1)
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SimplificationExample for POS (2)
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SimplificationDon’t-Care Condition
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SimplificationDon’t-Care Example (1)
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SimplificationDon’t-Care Example (2)