Building counters with flip-flops is not hard but easy. Then I show you a few counters that they count from 0-3, 0-4, 0-5, 0-6, 0-7, and two more from 0-9.
Step 1: Counter 0-3
This counter shows its schematic, plot of work, and equations. Note that it's only 2 flip-flops.
Step 2: Counter 0-4
This counter shows the same elements than the counter 0-3 but note that this needs 3 flip-flops for working.
Step 3: Counter 0-5
This counter also needs 3 flip-flops for working.
Step 4: Counter 0-6
Counter 0-6 is also a 3 flip-flop counter.
Step 5: Counter 0-7
You can realize counters from 0-4,......0-7 need 3 flip-flops for working and doing its sequential logic correctly.
Step 6: Counter 0-9
Counter 0-9 built with T-flip-flops and JK-flip-flops the fist and the second respectively and same also needs 4-flop-flop for working of right way.
SHOE0007 made it!