3. Design a combinational logic circuit that controls an elevator door in a three-storey building. There are 4 input conditions. M is a logic signal that indicates when the elevator is moving (M=1) or stopped (M=0). F1, F2 and F3 are floor indicator signals that are normally LOW, and they go HIGH only when the elevator is positioned at the level of that particular floor. i. Construct the truth table and simplify the Boolean expression into SOP form using K-map with don't care conditions. ii. Construct the logic diagram using AND-OR gate network with simplified SOP expression. iii. Construct the logic diagram using only NAND gates with simplified SOP expression