Q$1)$ Design a Mealy machine that detects two consecutive zeros, $"00",$ and outputs $"1"$ upon

detection. The machine should then reset and wait for the sequence again. Analyse the possibility

of state reduction for this Mealy machine. $($Total Score $=20$ Marks$)$

l$.$ Initially, draw the state diagram of the Mealy machine, assuming four states: Start $($S$),$ Zero

$1($ZI$),$ Zero $2($Z$2),$ and Reset $($R$).(4$ Marks$)$

$2.$ Derive the state table from the state diagram. $(8$ Marks$)$

$3.$ Analyze the state table for possible reduction. If possible, reduce the number of states and

redraw the minimal state diagram. $(8$ Marks$)$