1. Boolean Algebra

2. Boolean Algebra: Definition

3. Boolean Algebra: Theorem

4. Boolean Algebra & Logical Operator1 T F
Complement
0 = 1
0’ = 1
¬F = T
Sum + 
Product . 

5. Basic Boolean Algebra x y + . ↓
(NOR) ↑
(NAND) 1

6. Boolean Algebra
(x + y) . z = x . y + z (de Morgan Law)
Logical Operator
(x + y) . z = (x  y)  ¬z

7. Examples
(x + y) x
x ( y + z)
(x + y + z) (x y z)

8. Example

9. Example

10. Example

11. Boolean Function F(x,y,z)
F(x, y, z) = x.y + z

12. Disjunctive Normal Form
Problem:
Given the values of a Boolean functions, how can a Boolean expression that represents this function be found?
Any Boolean function can be represented by a Boolean sum of Boolean products of the variables and their complements  Disjunctive Normal Form (Sum-of-Products Expansions).

13. Disjunctive Normal Form
F(x,y,z) = x y z
G(x,y,z) = x y z + x y z

14. Disjunctive Normal Form
F(x,y,z) = (x + y) z
Find its Disjunctive Normal Form?
F(x,y,z) = x y z + x y z + x y z

15. Disjunctive Normal Form