Boolean Algebra
Boolean Algebra: Definition
Boolean Algebra: Theorem
Boolean Algebra & Logical Operator 1 T F Complement 0 = 1 0’ = 1 ¬F = T Sum + Product .
Basic Boolean Algebra x y + . ↓ (NOR) ↑ (NAND) 1
Boolean Algebra (x + y) . z = x . y + z (de Morgan Law) Logical Operator (x + y) . z = (x y) ¬z
Examples (x + y) x x ( y + z) (x + y + z) (x y z)
Example
Example
Example
Boolean Function F(x,y,z) F(x, y, z) = x.y + z
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).
Disjunctive Normal Form F(x,y,z) = x y z G(x,y,z) = x y z + x y z
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
Disjunctive Normal Form