A "majority circuit" is a combinational circuit whose output is 1 only when the input has more l's than 0's. Otherwise the output is 0. Design a 3-bit majority circuit and implement it using AND-OR logic. Show all steps of your work, including the truth table, K-Map simplification, Boolean expression and the logic diagram.

. Design a logic circuit that controls an elevator door in a three-story building. The circuithas four inputs. M is a logic signal that indicates when an 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 theelevator is positioned at the level of that particular floor. For example, when the elevator is lined uplevel with the second floor, F2=1 and F1=F3=0. The circuit output is the OPEN signal which isnormally LOW and is to go HIGH when the elevator door is to be opened.