Digital Electronics: State machine

[6021023]

Homework Statement

(a) How many states does this system have?
(b) How many rows will there be in a state transition table?
(c) Provide the state transition table.
(d) Draw a state diagram of the system.
(e) Describe what the circuit does in words.

Homework Equations

The Attempt at a Solution

a) I think there are two flip flops (or are they switches?), so that means that there are four states: 00, 01, 10, and 11.

b) I think the state transition table will have 8 rows. These numbers will be at the beginning of each row:

000
001
010
011
100
101
110
111

 

[berkeman]

Homework Statement

(a) How many states does this system have?
(b) How many rows will there be in a state transition table?
(c) Provide the state transition table.
(d) Draw a state diagram of the system.
(e) Describe what the circuit does in words.

Homework Equations

The Attempt at a Solution

a) I think there are two flip flops (or are they switches?), so that means that there are four states: 00, 01, 10, and 11.

b) I think the state transition table will have 8 rows. These numbers will be at the beginning of each row:

000
001
010
011
100
101
110
111

Good. Correct so far. Now make label those three columns as A, B and Y (the inputs to the logic), and make 2 more columns for the "Next X, Next Y" outputs of the FFs. Use the logic terms shown for the J&K inputs for the 2 FFs to calculate what the Next X and Next Y outputs will be for each row. That is your transition table. Then use that to answer the rest of the questions.

Show us what you end up with!

 

[6021023]

A B Y Next X Next Y
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

I'm a little bit confused as to what to do after this. I see the equation AB'Y + A'BY' going into J and K. So that means that J and K will always be the same. Is that right?

 

[berkeman]

A B Y Next X Next Y
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

I'm a little bit confused as to what to do after this. I see the equation AB'Y + A'BY' going into J and K. So that means that J and K will always be the same. Is that right?

Yes, from the diagram, it does appear that J and K for each FF are the same. What does a JK FF do when both inputs are the same?

 

[6021023]

When both J and K are 0, then there is no change in outputs.
When they are both 1, then the outputs are toggled.

A B Y Next X Next Y
0 0 0

I still get stuck at this part. I can tell that next Y is going to be 0, but I can't say what next X is, because the table doesn't tell me what X currently is.

Another question. Is the circuit a Mealy machine, since the output is going back into the input?