Question

1.Simplify the following functions using ONLY Boolean Algebra Laws and Theorems. For each resulting simplified function, sketch the logic circuit using logic gates. (30points)

a.SimplifyF= (A+C+D)(B+C+D)(A+B+C) Hint:UseTheorem8 ,theorem 7 and distributive

̅̅b. Show that (Z + X)(Z +Y)(Y + X) = ? ? + ? ?

̅̅c. Show that (X +Y)Z + XYZ = ?.?

(15 points for simplification and 15 points for Logisim diagrams)

2. Prove the below equation using Boolean Algebra Theorems and laws Write the name of rules applied for each step ( 5 points)

(A+B)(A+B)B=(A+B)(A B+BB) = 0

3. Write any valid Boolean expression for Q as a function of the input variable

Answer 1