3- Draw the logic circuit for the following equations. Apply De Morgan's theorem and Boolean Algebra rules to reduce them into equations having inversion bars over single variables only and then apply K-map to simplify the equations. Draw the simplified circuit. a) W = Ã+ B.BC + BC b) Z = ABC +D+ AB + BC

Q1 type answer only no need to explain

3. For the following truth table, C f 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 a ܘ ܘ ܘ 0 1 b 1100TOO TOTOTO 1) Show the sum of minterms in numerical form. 2) Show an algebraic expression in sum of minterms form and draw the logic diagram. 3) Simplify the sum of minterms form to a minimum SOP expression (three terms, six literals). Show each step of the simplification. Draw the logic diagram using the minimum SOP expression. 4) Show the product of maxterms in numerical form. 5) Show an algebraic expression for f in product of maxterm. 6) Simplify the product of maxterm form to a minimum POS expression for f (two terms, five literals). Show each step of the simplification.

7. (a) Prove with Boolean algebra that (x + y) + (y · x') = x + y. Give a reason for each step in your proof. (b) Show the dual proof of part (a).

3. (1 pt) Simplify the Boolean function using K-map. AB 00 01 11 10 1 1 1 1

Problem 1: Find the dual of a logic function F = (X'Y + Z)W’

Answer the following questions: a. Apply DeMorgan's Theorems to the following expression F = (ABC + DEF)' b. Apply DeMorgan's Theorems to the following expression F = ((A+B+C). D)' c. Use DeMorgan's Theorem in algebraic form to Prove F = A' + B' (A. B)' d. Use DeMorgan's Theorem in algebraic form to Prove F = A'. B' = (A + B)' e. Minimize the following Logic Expressions F, Y Algebraically and PROVE the function F to be equal to A'.C' + B, and the function Y to be equal to A+BC. A'.B'.C + A'.B.C'+A'.B.C+A.B.C'+A.B.C F (A, B, C) Y (A, B, C) (A+B) (A+C)

Provide the Boolean expression for X and simplify it. A O BO

6. (a) Prove with Boolean algebra that (x + y) (x' + y) = y. Give a reason for each step in your proof. (b) Show the dual proof of part (a).

Note: - You are attempting question 4 out of 12 Derive the hazard free Boolean expression for given logic function. F(W,X,Y.Z)= m(0,4,5,10,11,13,14,15) (а) АС + ВСD + ACD (b) АС + ВCD + ACD+АВС+ АBD (c) АС + ACD+ ABC + ABD (d) ABC + ABD Answer