Problem $4(25$ points$)$ em is about a circuit that has $4$ states $00,01,10$ and $11$ represented by Qi and Qo one output W$.$ The circuit is a counter and it behaves as follows has $2$ inputs $($S and T$)$ and When ST$-01$ the count is incremented by $2$: when ST$-10$ the count is incremented S $1-00$ the count remains the same, and when ST$-11$ the count is reset to $00.$ Example: suppose the current count or state is $01($decimal $1)$ then if input is $01,$ the next state is $11($decimal $3,$ an increment of $2)$; if th e input is $10,$ the next state is $10($decimal $2,$ an increment of $1)$; if the input is $00,$ the next state is $01($decimal $1,$ staying the same$),$ and if the input is $11,$ the count i $($decimal $0,$ reset$).$ done in any For the circuit described above, provide the following $($some of the items can be order$)$: $1.$ A state diagram. $2.$ A state transition table. $3.$ Minimized expressions for the next states. Use K$-$maps. $4.$ Construct circuits for each next state. $5.$ Assuming this circuit is to be implemented using D flip$-$flops $($one D flip flop for each bit of next state$),$ which variables in your circuit would you connect to the D inputs of the flip flops. Bonus: Complete the circuit implementation