GATE CS 2009 Q27 — Sequential Circuits

Given the following state table of an FSM with two states $A$ and $B$,one input and one output.

$$\small\begin{array}{|c|c|c|c|c|c|}\hline \textbf{PRESENT} & \textbf{PRESENT} & & \textbf{Next State } & \textbf{Next State} & \\ \textbf{STATE A} & \textbf{STATE B} & \bf {Input}& \bf {A} & \bf {B} & \bf{Output}\\ \hline \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{1} \\ \hline \text{0} & \text{1} & \text{0} & \text{1} & \text{0} & \text{0}\\ \hline \text{1} & \text{0} & \text{0} & \text{0} & \text{1} & \text{0}\\ \hline \text{1} & \text{1} & \text{0} & \text{1} & \text{0} & \text{0}\\ \hline \text{0} & \text{0} & \text{1} & \text{0} & \text{1} & \text{0} \\ \hline \text{0} & \text{1} & \text{1} & \text{0} & \text{0} & \text{1} \\ \hline \text{1} & \text{0} & \text{1} & \text{0} & \text{1} & \text{1} \\ \hline \text{1} & \text{1} & \text{1} & \text{0} & \text{0} & \text{1} \\ \hline \end{array}$$If the initial state is $A=0 ,B=0$ what is the minimum length of  an input string which will take the machine to the state $A=0,B=1$ with $output=1$.