It is required to design a synchronous sequential circuit that receives a serial input X that produces 1 when the input sequence is either {1001} (i.e., 1 followed by 0 followed by 0 followed by 1) or (0101} (i.e., 0 followed by 1 followed by 0 followed by 1) assuming overlapping sequences. Assume the existence of an asynchronous reset input to reset the machine to a reset state. The following is an example of an input/output stream: Examples: Input X 10010101001001 | Output Z 00010101001001 a) (10 points) Derive the state diagram of the circuit assuming a Mealy model. b) (15 points) Implement your design using D flip flops with minimal number of flip flops and combinational logic