VIRGIN 12:59 Welcome to your first assignment. This assignment consists efa mumber of "short-snapper questions on digital logic and Boolean algebra For each question, you must show all the necessary steps. Points wil be deducted for not showing steps Submission instructions: You may answer the questions hand-written on paper or you may use a word processor. In either case, collate afl your answers into one PDF document and upload it on Brightspace Make sure you enter your name and JD number on the header of the PDF document Late Policy: 10% per day late penalty on the assigninent score. For exampleif the score is 8/10 and the assignment is i day late, then the score wil be reduced to 72/10 Assignment submissions that are S days past the due date wWnot be accepted Question 1: Consider the following Boolean function: f (a, b, c) ab aabo a) Write the truth table for the function f b) Express the function f in the product of sums form. (Minimization not required) Question 2: Consider the following Boolean function: f (a, b, c, d)(b+d abc) a) Write the truth table for the function f b) Express the function f in the sum of products form. (Minimization not required). Question 3: Find the complement of the following expressions using DeMorgan's theorems: a) c)a+b+b+c) Question 4: Prove identity no. 17 in the list of identities from Boolean algebra that was discussed in the lectures: You may use any of the previous identities in your proof. Show step by step derivation of your proof and list the identity number that you have used in each step. Question S: We know that (AND, OR, NOT) is a functionally complete set. In the lectures we showed that (NAND) is a functionally complete set by showing how AND, and NOT can be implemented only with NAND gates. Similarly, we showed that (NOR) is a functionally complete set. Using a similar strategy a) Show that (OR, NOT) is a functionally complete set. b) Show that (AND, NOT) is a functionally complete set Question 6: Implement the Boolean function a) b) c) With AND, OR and NOT gates With OR and NOT gates With AND and NOT gates d) With NAND gates With NOR gates e) Question 7: Minimize the following Boolean functions using the algebraic method. d) 4 (a, b, c, d)2(0-3,5,7, 8-11, 13,15)