Design a $4-$bit counter with one input $($Start$),$ four negative$-$edge triggered J$-$K flip$-$flops, and basic

gates that will count down the $12$ Days of Christmas from $12$ to $1.$ Once the count is at $1,$ it should

remain in that state unless the input $$Start$$ is received $($pulse$)$ that will asynchronously restart the

counter to $12$ for the next countdown $($Hint: Use the asynchronous Preset and$/$or Clear input to reset

the latches when the Start input is received$).$