We intend to design using sequence detector DF$/$F$,$ which generates output y as $\text{'}1\text{'}$ when three or more $\text{'}0\text{'}$s are in succession from the input x$.($That is$,$ if the input x is O or $00,$ the output y must be $0$ and from the time x is $000,$ the output y must be $1.$ If the next input is $0,$ y remains $1,$ but if the next input is $1,$ y becomes $0,$ and returns to the initial state.$)$

a$)$ Draw a state diagram.

b$)$ Write a state table.

c$)$ Using K$-$map, simplify each F$/$Finput and output expression.

d$)$ Draw a sequence detector circuit using the D F$/$F and logic gate.

Please solve all of $4$questions.

When designing and drawing, I would appreciate it if you could write it by hand or use an easy$-$to$-$recognize program

Thank you!!