1. Logic Gates and Boolean Algebra
Chapter 4
Logic Gates and Boolean Algebra

2. Introduction
Logic gates are the actual physical implementations of the logical operators.
These gates form the basic building blocks for all digital logic circuits.
Logic gates process signals which
represent true or false.

3. Switch S1 AND Switch S2 must be closed to light the lamp
Introduction
Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX-NOR.
Switch S1 AND Switch S2 must be closed to light the lamp
Switch S1 OR Switch S2 (or both of them) must be closed to light the lamp

4. Truth Table
A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.

5. Logic Gates and Circuit Diagrams
OR Gate

6. Logic Gates and Circuit Diagrams
AND Gate

7. Logic Gates and Circuit Diagrams
NOT Gate

8. Logic Gates and Circuit Diagrams
NOR Gate

9. Logic Gates and Circuit Diagrams
NAND Gate

10. Logic Gates and Circuit Diagrams
EX-OR gate
The 'Exclusive-OR' gate is a circuit which will give a high output if either but not both, of its two inputs are high.
EX-NOR gate
is The inversion of EX-OR Gate

11. Describing Logic Circuits Algebraically

12. Describing Logic Circuits Algebraically

13. Evaluating Logic Circuit Outputs

14. Evaluating Logic Circuit Outputs

15. Determining Output Level from a Diagram

16. Implementing Circuits From Boolean Expression

17. Boolean Algebra Simplification of logical circuits.
One tool to reduce logical expressions is the mathematics of logical expressions.
The rules of Boolean Algebra are simple and straight-forward, and can be applied to any logical expression.

19. Boolean Algebra

20. Boolean Algebra

21. Boolean Algebra (A’B)’(A+B) Solution: (A + B’) (A + B)
AA + B’A + AB + B’B
A + B’A + AB
A + AB A
AB(A + B’C +C)
Solution:
ABA + ABB’C + ABC
AB ABC
AB + ABC AB

22. Boolean Algebra

23. Universality of NAND & NOR Gates

24. Universality of NAND & NOR Gates

25. Alternate Logic Gate Representations

26. Forms and Definitions of Boolean Expressions

27. Product of Sums Representation

28. Disjunctive Normal Form

29. Disjunctive Normal Form

30. Disjunctive Normal Form

31. Disjunctive Normal Form
Using truth tables, convert this expression into a sum of minterms