Tutorial 6 : Boolean Algebra

Exercise 1 1. Simplify the Boolean expression (x' + y)' + x'Ans: x' + y', which can also be written as (x × y)'2. Simplify the Boolean expression

[(x × z') × (y + x)] + (x × y')Ans: x × (y' + z'), or x × (y × z)'3. Use the laws of Boolean algebra to simplify

the Boolean expression x + [y × (y' + x)]1

Tutorial 6 : Boolean Algebra

Exercise 2 Write the Boolean function given by the following table in disjunctive normal form (Sum Of Product form)

x00001111

y00110011

z01010101

G00010011 2

Tutorial 6 : Boolean Algebra

Exercise 3Simplify the following Boolean expressions, and draw the digital circuits for both the original and simplified expressions :

Exercise 4Use Karnaugh maps to simplify the following Boolean expression :

3

)'(' yxxyx