Design a $4-$bit counter $F($ represented by $F_3{F}_2{F}_1{F}_0)$which can count the specified sequence as following:

$000010001111011010100000.$ 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$.R=0).$ 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$)$