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Is a K-map Sufficient for State Minimization in Digital Circuits?
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Discussion Overview
The discussion revolves around the sufficiency of using a Karnaugh map (K-map) for state minimization in digital circuits. Participants explore the relationship between state diagrams and K-maps, as well as alternative methods for minimizing states in the context of a specific problem involving state encoding and unused states.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Homework-related
Main Points Raised
- Some participants suggest starting with a state diagram to determine how outputs map to states before applying a K-map for minimization.
- Questions arise about the consideration of present states when constructing the state diagram, with some affirming that transitions depend on the current state and input values.
- There is a query regarding alternative methods for minimizing the number of states beyond using a K-map.
- Concerns are raised about the presence of unused states in the state machine, with suggestions that these should be accounted for to avoid potential stalling in the machine's operation.
- Some participants note that the problem specifies a certain number of states, which may influence how the state diagram is constructed and whether unused states are a concern.
Areas of Agreement / Disagreement
Participants express differing views on the necessity of considering unused states and the effectiveness of K-maps for state minimization. The discussion remains unresolved regarding the best approach to handle unused states and the overall sufficiency of K-maps in this context.
Contextual Notes
Participants highlight the importance of understanding the relationship between present states and transitions, as well as the implications of unused states in state machines. There is a lack of consensus on how to best approach the minimization problem presented.
- #2
berkeman
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jazzel70 said:
I would draw the state diagram first to see if the outputs map directly to states (or if more logic is needed), then use a K-Map to help with minimization.
How many states are in the table? How many bits will it take to encode those states? Are there any unused states left over? If so, you will need to handle that...
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jazzel70
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do you consider the present states when doing the state diagram?
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berkeman
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jazzel70 said:
Yes, you transition between the present state and the next state according to the table, based on the input value.
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jazzel70
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is there another way of minimising the number of states?
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berkeman
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jazzel70 said:
The number of states is given in the problem statement. Well, you would also normally add the extra states into the diagram for the unused states (the problem calls for 6 states, which leaves 2 unused states). You cannot allow unused states in a real state machine, because that could cause the machine to stall forever if it ever gets into one of those states. You generally have the unused states have transitions back into the other states (preferably the Reset state).
But in this simpler problem, they don't seem concerned about the unused states. Do you have an initial implementation of the state diagram?
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