Design a $4-$bit synchronous counter that counts the prime integer numbers greater than one and less than $15.$ The counter shall start counting from the smallest prime integer up to the greatest prime integer in the above range. Once the counter reaches the greatest prim integer, it goes back and starts counting from the smallest prime integer. Use JK flip flops and any necessary logic gates to build this counter.

a$.$Only SOLVE E

e$.$ Use k$-$maps to find the equations of the flip flop inputs.

f$.$ Plot the logic circuit of your counter.