Questions 1. Given the Boolean function Let F=2.1.+2.9.2+2-y. a. List the truth table for the function b. Draw the logic diagram using the original Boolean expression. (Use Digital) C. Simplify the algebraic expression using Boolean algebra d. List the truth table of the function from the simplified expression and show that it is the same as the truth table in part (a) e. Draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part (b). (Use Digital) 2. With the following circuit: A B C O a. Find the algebraic function for the circuit b. Reduce it down to at most two gates by using a K-Map c. Prove that a and b are equivalent d. Draw the new circuit in Digital 3. Simplify the following Boolean functions using k-maps. Prove each with truth table. Draw each circuit in Digital a. F(x, y, z) = (0,2,3,4,6) b. F(A,B,C,D)=(0,2,8, 10, 15) 4. With the following Boolean function with the don't care conditions d. F(W, 2, 4,2)=(0, 1, 2, 3, 7, 8, 10) d(u, I, y, z)=(5, 6, 11, 15) a. Build a truth table b. Write the non reduced algebraic function for F c. Reduce using a K-Map d. Draw the circuit for F found in c. Deliverables