Electrical – Design 5 bit counter with two control inputs (direction and stop)

Serial/parallel-load shift registers and bit rotations are going to work most naturally with a D flip flop, since they just send data straight through; binary counters are going to work most naturally with a T flip flop, since each counter bit C_k = C_k,previous XOR carry_k, where carry is the carry bit from the previous stage.

If you look at JK flip-flops, however, they are the "universal" flip-flop that can act as a D- or T- flip-flop depending on the input signals.

To get a D from a T, or vice versa, you need an XOR gate. To get a T from a JK, you just tie the JK inputs together. To get a D from a JK, you need an inverter, as the J/K inputs need to be opposites.

In your application, you've got enough complexity, that I suspect the gate counts are going to be very close, and it's probably not worth worrying about -- unless you have to optimize, in which case you'll just have to try it for each case.

IMHO, the D flip-flop is conceptually the simplest to use, and it works naturally with most of your operations, so I'd start with that.

The "trick" with JK flip-flops

Since we don't have a previous answer about designing state machines with JK flip-flops...

Designing with JK flip-flops is pretty much the same as design with D flip-flops (or T flip-flops or any other kind of flip-flops.) But with the JK flip-flop the excitation table is such that there is a trick that makes dealing with the state transition logic slightly simpler.

For any state machine/counter design you need the excitation table for your particular flip flop.

For JK flip flops the excitation table looks like

Previous State -> Present State    J K
0 -> 0                             0 X
0 -> 1                             1 X
1 -> 0                             X 1
1 -> 1                             X 0

The special property we are going to leverage is that when the previous state is 0 then the K input is a don't care, and when the previous state is 1 then the J input is always a don't care.

First you have to complete your table. Not only do you have to have the inputs and the Qs, you also need all the J and K entries:

x|y|Q1|Q2|Q3||Q1+|Q2+|Q3+||J1|K1|J2|K2|J3|K3
--------------------------------------------
0|0|0 |0 |0 || 1 | 1 |0  ||1 |X |...
0|0|0 |0 |1 || 0 | 0 |0  ||0 |X |
0|0|0 |1 |0 || 0 | 0 |1  ||0 |X |
0|0|0 |1 |1 || 0 | 1 |0  ||0 |X |
...

Now we need to draw the 6 K-Maps for J1,K1,J2,K2,J3, and K3. If we weren't using our "trick" we would need these to be 5-variable maps (x,y,Q1,Q2, and Q3).

But because J1 is don't care whenever Q1 is 1 we only need to do the map for J1 for the case that Q1 is 0. And of course, in that case we know that Q1 is 0, so we can just do a 4 variable map (with input variables x,y,Q2, and Q3).