Boolean Algebra

Chapter 3

Boolean ValuesIntroduction

Boolean OperationsFundamental Operators

Boolean OperationsBinary Boolean Operators

Boolean AlgebraPrecedence of Operators

Boolean AlgebraFunction Evaluation

Boolean AlgebraBasic Identities

Boolean AlgebraDuality Principle

Boolean AlgebraFunction Manipulation (1)

Boolean AlgebraFunction Manipulation (2)

Boolean AlgebraFunction Manipulation (3)

Standard FormsSOP and POS

Standard FormsMiniterms

Standard FormsSum of Minterms

Standard FormsMaxterms

Standard FormsProduct of Maxterms

Standard FormsMinterm and Maxterm Exp.

Standard FormsForming Sum of Minterms

Standard FormsForming Product of Maxterms

Standard FormsConverting MIN and MAX

SimplificationKarnaugh Maps

SimplificationKarnaugh Map Ordering

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.

SimplificationProcedure for SOP

SimplificationExample for SOP (1)

SimplificationExample for SOP (2)

SimplificationProcedure for POS

SimplificationExample for POS (1)

SimplificationExample for POS (2)

SimplificationDon’t-Care Condition

SimplificationDon’t-Care Example (1)

SimplificationDon’t-Care Example (2)