Design a $4-$bit counter that can count either up or down up to $13$ on the rising edge of the clock.There are three input signals: a clock signal, a reset signal, and a signal to indicate whether thecounter should count up or count down. If the up$/$down signal is high, the counter will count up$,$ ifthe input signal is low, the counter will count down. On reset, the count will return to zero.

$($a$)$ Give the state table for this sequential circuit.

$($b$)$ Use K$-$maps to find the MSP expressions to be used as inputs to the D flip$-$flops.

$($c$)$ Draw the logic diagram for this counter.

$($d$)$ Draw the state diagram for this circuit