This document covers the topics of Boolean algebra including Boolean values, fundamental operators, precedence of operators, function evaluation, identities, and manipulation. It also discusses standard forms such as sum of products (SOP) and product of sums (POS), minterms, maxterms, and converting between standard forms. Additional sections cover Karnaugh maps, implicants, simplification procedures for SOP and POS, and examples of simplification including with don't care conditions.

1. Boolean Algebra
Chapter 3

2. Boolean Values
Introduction

3. Boolean Operations
Fundamental Operators

4. Boolean Operations
Binary Boolean Operators

5. Boolean Algebra
Precedence of Operators

6. Boolean Algebra
Function Evaluation

7. Boolean Algebra
Basic Identities

8. Boolean Algebra
Duality Principle

9. Boolean Algebra
Function Manipulation (1)

10. Boolean Algebra
Function Manipulation (2)

11. Boolean Algebra
Function Manipulation (3)

12. Standard Forms
SOP and POS

13. Standard Forms
Miniterms

14. Standard Forms
Sum of Minterms

15. Standard Forms
Maxterms

16. Standard Forms
Product of Maxterms

17. Standard Forms
Minterm and Maxterm Exp.

18. Standard Forms
Forming Sum of Minterms

19. Standard Forms
Forming Product of Maxterms

20. Standard Forms
Converting MIN and MAX

21. Simplification
Karnaugh Maps

22. Simplification
Karnaugh Map Ordering

23. Simplification
Implicants
• Implicant
A product term is an implicant of a function if the
function has the value ‘1’ for all minterms of the product
term.
• Prime implicant
If 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 implicant
A prime implicant that covers a ‘1’ square which is not
covered by no other prime implement rectangles.
• Non-essential prime implicant
A prime implicant in which all of its covered ‘1’ squares
are covered by one or more other prime implicants.

24. Simplification
Procedure for SOP

25. Simplification
Example for SOP (1)

26. Simplification
Example for SOP (2)

27. Simplification
Procedure for POS

28. Simplification
Example for POS (1)

29. Simplification
Example for POS (2)

30. Simplification
Don’t-Care Condition

31. Simplification
Don’t-Care Example (1)

32. Simplification
Don’t-Care Example (2)