Design Mod$-6$ synchronous down counter using $T$ master slave FF$.$ The counter continuously counts, starting from $0,$ going to $0-5-4-3-2-1-0$ and then back to $5.$ Each FF in the clock cycle In order for it to switch, $T$ input must be $"1".$

a$.$ Create the truth table of the counter.

b$.$ Simplify using Karnaugh diagram to design the meter.

c$.$ Verify the counter design using Logisim. $(30$ points$)$