In mathematics, the Fibonacci numbers form a sequence, the Fibonacci sequence, in which each

number is the sum of the two preceding ones. The sequence commonly starts from $0$ and $1.$ The first

few values of the sequence are $0,1,1,2,3,5,8,13,21,34,55,89,144.$ Now design a synchronous

counter for counting the following Fibonacci sequence using the T flip$-$flop and basic gates.

Sequence: $1=>2=>3=>5=>8=>13=>1=>2=>$dotsdotsdots

$($a$)$ Draw the State Diagram.

$($b$)$ Find the State Table with T flip$-$flop inputs.

$($c$)$ Minimize the functions of T flip$-$flop inputs.

$($d$)$ Draw the logic diagram using $T$ flip$-$flops and basic gates.