$($Part A $-8$ Points$)$ Find the state table for the following sequential circuit built with $\backslash (1$ J K $\backslash )$ and $\backslash (1$ T $\backslash )$ flip$-$flop. Assume that a state is represented as $\backslash ($ Q$\_\{1\}$ Q$\_\{0\}\backslash ).$

$($Part B $-8$ Points$)$ The following FSM takes a $1-$bit input $\backslash ($ X $\backslash )$ and produces a $1-$bit output $\backslash ($ Z $\backslash ).$ Implement the FSM with an SR flip$-$flop. $($Part C$-8$ Points$)$ A new type of MN flip$-$flop has been proposed which supports the four operations of set, reset, hold, and toggle. The following FSM has been implemented with the MN flip$-$flop, resulting in the following next state logic for $\backslash ($ M $\backslash )$ and $\backslash ($ N $\backslash ).$ Please recover the characteristic table of the MN flip$-$flop.

$($Part D $-10$ Points$)$ Another new type of $\backslash ($ V W $\backslash )$ flip$-$flop has been developed to implement the following state graph into the following circuit. Assume that a state is represented as $\backslash ($ Q$\_\{1\}$ Q$\_\{0\}\backslash ).$ Please identify the excitation table of the VW flip$-$flop.