(Solved): 4(a) Design a synchronous counter with an external input X. When X=1 the counter goes through the s ...

4(a) Design a synchronous counter with an external input $X$. When $X=1$ the counter goes through the sequence $1,4,3,6,2,5$ and repeats. With $X=0$, the counter counts in the reverse direction. For states $0\&7$ assume don't cares as your next states. Design the counter using D flip-flops and minimum logic gates. Draw the logic diagram. Show all steps. (b) In your design, what happens if the counter starts in ' 0 ' state with $\mathrm{X}=1$ on power up? (Answer this part once your design is completed.)