The $\text{mod}-5$ counter shown in the figure is counts through states $Q_{2} Q_{1} Q_{0}=000,001,010,011$ and $100$
(a) Will the counter lockout if it happen to be in any one of the unused states?
(b) Find the maximum rate at which the counter will operate satisfactorily. Assume the propagation delays of fliplop and $\text{AND}$ gate to be $t_{F}$ and $t_{A}$ respectively.