What is an implication chart?
Implication charts are a common way of reducing an FSM. It works by finding states that have identical transitions to each other. It is a graphical method suitable for fast computation by hand. First, lets consider a grid of size N×N, where N is the number of states. Each cell represents a pair of states.
How can we reduce the state table?
To minimize the number of states, we will identify “equivalent states” and eliminate any redundancy found. Two states are equivalent if they have equivalent next states and the same output for each possible input condition.
Which method is used for reducing the number of states?
It is therefore desirable to know when two or more states are equivalent in all aspects. The process of eliminating the equivalent or redundant states from a state table/diagram is known as state reduction. Example: Let us consider the state table of a sequential circuit shown in Table 6….
| B | C |
|---|---|
| A | D |
| D | E |
| A | E |
| A | D |
What are the benefits of state reduction?
State reduction technique also allows you to be less meticulous in obtaining the initial finite state machine description. If you have introduced a few redundant states, you will find and eliminate them by using the state reduction technique introduced next.
What is the advantage of state reduction?
How to create an implication chart for state reduction?
1.Construct implication chart, one square for each combination of states taken two at a time . 2.Square labeled Si, Sj, if outputs differ then the square gets an ‘X’. Otherwise, write down implied state pairs for all input combinations . 3.Advance through chart top-to-bottom and left-to-right.
How are the number of States reduced in studytronics?
In this particular example, the number of states was reduced from fifteen (15) to seven (7) states. This literally amounts to a reduction of eight (8) states and the elimination of one flip-flop for the final design. The implication chart method uses a graphical grid of sorts to systematically find equivalences among the states.
How does successive partitioning reduce the number of States?
Successive partitioning is almost a cross between row matching and implication chart where both a graphical table and equivalent matching is used. Each of these methods will, in most cases, reduce a state machine into a smaller number of states. Keep in mind that one method may result in a simpler state machine than another.
Which is an example of an implication chart?
The implication chart assists in keeping track of any implications such as, for example, c-d and e-f are implied pairs for a-b in Table 4 below: Focusing attention towards a different example, the implication chart method will be demonstrated in more detail.