Digital Electronics: State machine

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Discussion Overview

The discussion revolves around a homework problem related to digital electronics, specifically focusing on state machines. Participants are tasked with determining the number of states, constructing a state transition table, and drawing a state diagram, while also describing the circuit's function.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the system has four states based on the presence of two flip-flops, represented as 00, 01, 10, and 11.
  • There is a suggestion that the state transition table will contain eight rows, listing binary combinations from 000 to 111.
  • One participant expresses confusion regarding the next outputs of the flip-flops and questions whether the inputs J and K will always be the same based on the provided equation.
  • Another participant confirms that J and K being the same leads to specific behaviors of the JK flip-flop, noting the conditions under which outputs change or toggle.
  • A later reply raises a question about whether the circuit qualifies as a Mealy machine, suggesting that the output feedback into the input may indicate this classification.

Areas of Agreement / Disagreement

Participants generally agree on the number of states and the structure of the state transition table. However, there is uncertainty regarding the behavior of the JK flip-flops and the classification of the circuit as a Mealy machine, indicating that the discussion remains unresolved on these points.

Contextual Notes

There are limitations in the discussion regarding the current state of the outputs, which affects the ability to determine the next states accurately. Additionally, the definitions of Mealy and Moore machines are not fully explored, leaving some ambiguity in the classification of the circuit.

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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.

y2002p2q3.png


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
 
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6021023 said:

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.

y2002p2q3.png


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!
 
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?
 
6021023 said:
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?
 
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?
 

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