ABCD counter with a four$-$bit output representing the $BCD$ code for the number of pulses that have been applied to the counter input. For example, after four pulses the counter outputs are DCBA$=0100($base$2)=4.$ The counter resets to $0000$ on the tenth pulse and starts counting over again. In other words the DCBA outputs will never represent a number greater than $1001($base$2)=9.$

PartA: Design the logic circuit that produces a HIGH output whenever the count is $2,3,$ or $9.$ Use K$-$mapping and take advantage of the don't care conditions. Remember to add in the Don't Cares.

PartB: Repeat for $x=1$ when DCBA$=3,4,5,8$