Moore to Mealy Machine Conversion

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Both Mealy and Moore machines generate outputs from the finite state machine. In this chapter, we will explain how to convert a Moore machine to a Mealy machine. We'll use the state diagram of the Moore machine as our starting point and learn how to convert it into the equivalent state diagram of the Mealy machine.

Concepts for Moore and Mealy Machines

In a Moore machine, the output is represented on the state itself. In contrast, in a Mealy machine, the output is represented on the transition, or in other words, on the arrow itself.

Compared to the Mealy-to-Moore conversion, this Moore-to-Mealy conversion is relatively simple. Let us take a look at the conversion rules.

Basic Conversion Rules

Converting a Moore machine to a Mealy machine is simple. The key is to transfer the output information from the states in the Moore diagram to the transition arrows in the Mealy diagram. Here are the rules −

Rule 1: Incoming Transitions

For each state in the Moore diagram, check its incoming transitions.

Imagine a state 'A' with two incoming transitions. In one transition, the input is '0', while in the second transition, the input is '1'. Let's say the output of the machine in state 'A' is '1'.

In the equivalent Mealy representation, we'll write the '1' alongside the input for both transitions. This '1' represents the output during each transition leading to state 'A'.

If the output of the machine in state 'A' was '0' instead of '1', we would write '0' alongside the input for both transitions.

Rule 2: Outgoing Transitions and Outputs

Once we've covered all the incoming transitions to a state, we move on to the outgoing transitions from that specific state.

Let's say state 'A' has two outgoing transitions. Imagine the output '1' is within state 'A' itself, and there's a transition from 'A' to state 'B'.

In the equivalent Mealy diagram, the transition looping back to state 'A' will have the output '1' associated with it, as that's the output of the machine in state 'A'.

The outgoing transition from 'A' to 'B' will have the output associated with state 'B' in the Moore diagram. If state 'B' has an output of '0', then the transition from 'A' to 'B' will have '0' written on it in the Mealy diagram.

Example of Moore to Mealy Machine Conversion

Let us understand the idea through an example for a better understanding. Consider we have a Moore machine state diagram with three states.

State Transition Table

The state transition table is like below −

Now let us try to make the Mealy machine diagram corresponding to the previous Moore diagram.

When we convert a Moore machine to a Mealy machine, the number of states in the equivalent Mealy machine will be less than or equal to the Moore machine.

After converting the Moore machine to a Mealy machine, it's essential to check for redundant states in the state diagram.

• Identify Identical Rows − Analyze the state table for rows with identical next states and outputs for each input. These rows indicate redundant states.
• Remove Redundant States − Choose one of the redundant states and replace all its instances in the state table and diagram with the other identical state.
• Simplified State Diagram − The resulting state diagram with the removed redundant state represents the simplified Mealy machine.

Let us see another example with five states.

Now let us convert to Mealy −

In the table, the states 'B' and 'E' have identical next states and outputs for both input values (0 and 1). So we can reduce them by removing state 'E' from the state table and diagram, replacing its instances with state 'B'.

Conclusion

Converting a Moore machine to a Mealy machine is a straightforward process. We just need to analyze the incoming and outgoing transitions carefully and then associate the output based on the states in the original Moore diagram.

After the conversion, we should check for and remove redundant states to obtain a simplified and efficient Mealy machine representation to make it efficient.