You are tasked to design a $3$ bit counter, the counter will have three D Flip.Flops $A_2,A_1,$ and $A_0.$ for every single CLK pulse, its value increases by $1.$ Say at time $0,A_2{A}_1{A}_0=000,$ then the next time step it should be $001,$ and the next $010,$ so on$.$

A$.$ Assuming the next states are $D_2,D_1,$ and $D_0.$ derive the state diagram for the circuit $(1$pt$).$

B$.$ Assume you have an additional input $x,$ which when it's equal to $1$ changes the next state to $000$ regardless of current state. Find the boolean expressions $(1$pt$),$ then draw the circuit diagram and save it as e$3.$ cet $(2$pt$).$

Requirement: you must show the implemented component tested using a switch for $x,$ and a Hex display for showing the current state.