A synchronous sequential circuit is given with a one-bit input m and a three-bit output Y. When m = 0, the output follows the sequence: 011, 101, 110, and then the sequence repeats. When m = 1, the output sequence changes to 001, 010, 100. a) Draw and describe briefly the state diagram of the circuit. b) Derive optimized Boolean equations describing the next-state logic of the circuit. Every missing piece of information you need to supplement by yourself. Explain each design decision.

Design a logic circuit that illustrates Rule 11 of Boolean algebra: A+ AB = A + B A pulse generator is used to represent the input A and a switch is used for the input B. Switch B is open for B = 1 and closed for B = 0. Draw the logic circuit. Also, draw the timing diagrams for the following scenarios: i. B = 0 ii. B = 1

. 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.

Design a Moore state machine with one input x, and one output y. The output is normally 0, but becomes 1 whenever the machine detects the sequence "x = 0", "x = 1", and "x = 1" on the three consecutive rising edges of the clock.  Sketch a state graph for your design. Write down the state table for your design Come up with a state assignment Find the excitation logic for D flip flips Sketch a diagram of your final design.