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Boolean Algebra Chapter 3

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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)