Design a Mealy, nonresetting finite state machine that has one binary input X and one binary output Z. The output Z = 1 occurs whenever the last five bits on input X have been 11101; otherwise, the output Z = 0. This machine recognizes overlapping sequences also. For example, if the input sequence is X = 11101110111110111010, then the output sequence is Z = 00001000100000100010. Design the circuit that implements the FSM with DFFs and minimum number of other gates.