Using JK flip$-$flops design a modulo$-8$ counter whose specification is as follows:

Input : $x(t)in\{0,1\}$

Output: $z(t)in\{0,1,2,3,4,5,6,7\}$

State: $s(t)in\{S_0,S_1,S_2,S_3,S_4,S_5,S_6,S_7\}$

Initial state: $s(0)=S_0$

Function:The system counts modulo$-8$ number of $1\text{'}$s in the input sequence.