Finite State Machine Design
The Finite state machine design process consists of
1. Constructing an initial state machine that realizes the design.
2. Minimizing the number of states.
3. Encoding the states.
4. Choosing the memory device to implement the state memory.
5. Implementing the finite state machine’s next state and output functions.
In the age of very large scale integrated circuits, why should we bother to
minimize a state machine implementation? After all as long as the input/output behavior
of the machine is correct, it doesn’t matter how it is implemented. Or does it?
Advantages of minimum states
In general, you will find it is worthwhile to implement the finite state machine in as
few states as possible. This usually reduces the number of gates and flip-flops you need
for the machine implementation. For example, you are given a finite state machine with 18
states, thus requiring five state flip-flops. If you can reduce the number of states to 16 or
less, you save a flip-flop. Even if reducing the reducing the number of states is not enough
to eliminate a flip-flop, it still has advantages. With fewer states, you introduce more don’t
care conditions into the next-state and output functions, making their implementation
simpler. 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.
State Minimization
State reduction identifies and combines states that have equivalent behavior. Two
states have equivalent behavior if, for all the input combinations, their outputs are the
same and they change to the same or equivalent next states. Algorithms for state reduction
begin with the symbolic state transition table. First we group together states that have
same state outputs (Moore machine) or transition outputs (mealy machine). These are
potentially equivalent, since states cannot be equivalent if their outputs differ. Next, we
examine the transitions to see if they go to the same next state for every input
combination. If they do, the states are equivalent and we can combine them into a renamed
new state. We then update all transitions to the newly combine states. We repeat this
process until no additional states can be combined.
There are two common methods by which states can be minimized.
1. Row-matching method.
2. Chart method.
