Sequential Design Help

In one respect, it is as simple as Z = XB, the problem is that B is not one of the inputs and we want to know what the output of the system is as a function of what we feed into it. In a sequential machine, it's not just the current inputs, but also all of the previous inputs. The cumative effect of the previous inputs is captured by the present state, which is the set of values of the memory elements (the flip flops). Since you have two memory elements, you have, at most, four states.

So what you need to do is, for each of the possible states, draw a truth table that what the next state (i.e., the next values of A and B) is going to be as a function of the two inputs X and Y. You can also determine the output, Z, in each state as a function of the state and of X.

 

Question No1 is a bit obscure in a sequential circuit.

I would indeed say that Z=BX. There is recursiveness in the solution that doesn't allow a closed expression

A state table is a more complete way to describe the circuit. Use X, Y, A and B as inputs and A', B' and Z as outputs.

If state machines is your topic this week, check this tutorial if you want. Note, however, that it is for Moore machines and this is a Mealy one.
http://www.allaboutcircuits.com/vol_4/chpt_11/5.html

@WBahn
Hey! It's been a long time since we were in a thread together.

 

I definitely see your point and, for the level of course that this one is, this may well be the best answer for that part of it.

Another part of me wanted to say that, since this is a finite automaton, that it can be described by a regular expression. But I'm not at all certain that being a Mealy machine doesn't complicate things considerably. Even if that weren't the case, the more I think about it the more this seems like apples and oranges.

That is has! I've seen you around, but generally have felt like I had nothing useful to add.

 

For me the problem isn't the Flip Flops. We could very well make reference to the state of A or B one or two pulses back. Here, both A and B have feedback loops for B.

I tried to write this:

but then I thought about the circuit with one D-FF. D=(X XOR Q), Y=Q'.

You really can't know the output if you don't have the initial condition.

 

Yep. To use a regular expression (which is pretty much exactly what you are talking about) you have to have a start state. I would have just assumed a start state of A=B=0, but there is really no justification for doing so when the problem doesn't indicate it. In theory, you could come up with something for each possible initial condition, but that is not practical.

So, yeah, I think the state diagram and/or state transition table is the best way to capture the relevant behavior of the machine.