Design a three$-$bit down counter using three D flip$-$flops $($A $,$ B and C$)$ and a U input. This counter has $5$ states $101,100,011,010,001.$ When input U$=1,$ the counter counts down, i$.101,100,011,010,001$ and back to $101$ and when input U$=0,$ the counter does not change.

a$)$ Create the state diagram

b$)$ Complete the state table below from the excitation table of part a

c$)$ Create K$-$Maps for the inputs by completing the following K Map tables using data in the table of part b