Designing state machine for Jk FF Counter

The counter is supposed to go from 1>3>4>7>6 and use JK flip flops.

While filling out the state table I'm a bit confused about what to do with invalid states. Since I think this is 3 bits and should use 3 FFs I have columns for present state, next state, and FF inputs: A B C An Bn Cn Ja Ka Jb Kb Jc Kc. I just wrote invalid for the next states that aren't included in the state diagram, but what do I do for the FF inputs, are these invalid too or don't cares? And if invalid, does that count as a zero when solving for their equations using kmaps? Any help is appreciated, thanks.

Answer

You can use two methods to solve this.

1. Use a self starting counter. In this case the invalid states are also included while preparing the truth table. The next state for an invalid state can be any valid state.Usually it is taken as the nearest valid state.


2. Non self starting counter in which you don't include the invalid states.While drawing the k-map, cells corresponding to invalid states are considered don't care.