Design a "Sequence Recognizer" that can recognize the occurrence of a particular sequence of bits, regardless of where it occurs in a longer sequence. This recognizer has one input $x$ and one output $Z.$ It has reset applied to the direct reset inputs on its $D-$ flip flops to initialize the state of the circuit to all zeros. The circuit is to recognize the sequence $"0101"$ by making output equal to one otherwise the output will remain zero.

a$)$ Draw State Diagram for the Sequence Recognizer.

b$)$ Draw two$-$dimensional State Table.

c$)$ Determine the Input and Output Equations.

d$)$ Draw complete Sequential Circuit.