A given FSM has an input, w, and an output, z. During four consecutive clock pulses, a sequence of four values of the w signal is applied. Derive a state table for the FSM that produces z=1 when it detects that either the sequence w:0010 or w:1110 has been applied; otherwise, z=0. After the fourth clock pulse, the machine has to be again in the reset state, ready for the next sequence. Minimize the number of states.