How to convert the Moore machine to the Mealy machine

Moore machines can be converted to Mealy machines with a few simple steps. We know that Mealy machines are faster, so we may want to convert our Moore machine to a Mealy machine.

Note: You can learn more about Moore machines and Mealy machines.

Conversion techniques

There are two techniques to convert these machines:

• By transition diagram

• By transition table

Let's take examples of both of these techniques.

By transition diagram

The steps involved in this method are:

1. To redraw the original states without the output. The starting state remains the same.

2. Draw the transitions as they are on the original machine.

3. Add output to the transitions based on their destination's output symbol in the original machine.

Example

Let's take a simple Moore machine:

1. We redraw the states without the output:

2. Draw transitions:

3. Now we add output to the transitions based on the transition's destination:

For example, the output of the transition $q_0 \to q_1$ is $b$, because the transition lands on $q_1$ which had an output $b$ in the original Moore machine.

The transformed machine above is our final Mealy machine.

By transition table

The steps involved in this method are:

1. To rewrite the table, excluding the output column.

2. To add the output to the destination columns adjacent to the destination state. The output will be according to the output of the destination state in the Moore machine transition table.

Example

Let's take the transition table of the previous example is:

1. We will rewrite the table above without the output table:

2. Now, we'll add the output symbols to the destination symbols by looking at the original table:

For example, for $q_0$, the destination state for $1$ is $q_1$. As a result, we see that the output against $q_1$ in the original table is $b$, so the output here will also become $b$.

This is the final transition table of the Mealy machine.

Conclusion

While transforming a Moore machine having $n$ states and $m$ outputs, there can be at most $n$ states in the Mealy machine.