Project$\_$C

Design a $4-$bit counter $C($ represented by $C_3{C}_2{C}_1{C}_0)$ which can count the specified sequence as following: $000001101001001011000000.$ The counter will use the falling edge of the clock $($ denoted by Clk$)$ and have a separate reset pin $(R)$ which will reset the counter to $0000$ when it is low $($e$.$g$.=0).$ Please use D type Flip$-$flops. Write down the state diagram, and state table; Use K$-$map to simplify the input equations; Write down the simplified input equations and draw a neat circuit diagram. $($Hint: use don't care for unused states$)$