Design, implement, and simulate modulo $4$ counter $(0,1,2,3,0,....)$ using DFFS$.$

a$)$ Show the state diagram.

b$)$ How many DFFS are needed?

c$)$ Show the state table.

d$)$ Show the characteristic table.

e$)$ Show the logic equations for the input of each DFF$.$

f$)$ Show the overall logic of the Counter.

g$)$ Verify your design using Logisim.