Step 1:

Determine the number of flip flop needed

Flip flop required are

$2^n ≥ N$

Mod 5 hence N=5

$\therefore 2^n \underline{\gt} N \\ \therefore 2^n \underline{\gt} 5 \\ N=3 \hspace{0.2cm} \text{i.e. 3 flip flop are required}$

Step 2:

Type of flip flop to be used: JK flip flop

Step 3:

1) Excitation table for JK flip flop

Now, we can derive excitation table for counter using above table as follows:

2) Excitation table for counter

Step 4

K-map simplification

For $J_C$

$J_c=Q_BQ_A$

For $K_C$

$K_C=1$

For $J_B$

$J_B=QA$

For $K_B$

$K_B=QA$

For $J_A$

$J_A=\overline{Q}_C$

For $K_A$

$K_A=1$

Step 5 Logic Diagram

Step 6: Timing Diagram