Last Updated on December 27, 2023 by Ankit Kochar
In the realm of digital systems and automata theory, Mealy and Moore machines stand as two fundamental models that describe the behavior of finite state machines. These machines play a crucial role in designing and understanding sequential circuits and systems. The primary distinction between Mealy and Moore machines lies in the way they handle outputs in response to inputs. Mealy machines produce outputs that depend on both the current state and the input, while Moore machines generate outputs based solely on the current state. This exploration delves into the intricacies of Mealy and Moore machines, elucidating their differences, applications, and implications in the context of digital system design.
What is Finite State Machine?
There are two types of finite state machines Moore and Mealy, before diving deep into the difference between mealy and Moore machines let us first understand what are Finite State Machines (FSM). Finite State Machine is the simplest machine that is used to recognize patterns. It is an abstract computing device that has five tuples.
Formal Definition of Finite State Machine
It is defined as a set of five tuples or elements
M=(Q, Ξ£, Ξ΄, q0, F)
where,
Q: Finite set of states.
Ξ£: Finite set of alphabets called input symbols.
Ξ΄: Q Γ Ξ£ β Q Transition function.
q0: Initial state.
F: Set of Final state.There are two types of finite-state machines and the main difference between them is the way the output is generated in the machines.
- Moore Machine
- Mealy Machine
What is Moore Machine?
A finite state machine with an output symbol for each state is known as a Moore machine. The current state and current input symbol decide the next state in a Moore machine.
The present state of the machine determines the output symbol at a given time.
Moore machine consists of six tuples which are :
(Q, q0, Ξ£, O, Ξ΄, Ξ»)Where,
Q: Finite set of states.
q0: Initial state
Ξ£: Finite set of alphabets called input symbols.
O: Output alphabet.
Ξ΄: Transition function where Q Γ Ξ£ β Q.
Ξ»: Output function where Q β O.Example 1
Design a Moore machine to generate 1βs complement of a given binary number.
Answer
The transition diagram is as follows β
Explanation:
- Step 1 – The start state q0 generates output 0 and transitions to q1 on input ‘0’, and transitions to q2 on input ‘1’.
- Step 2 – The state q1 generates output 1 and transitions to itself on input ‘0’, and transitions to q2 on input ‘1’.
- Step 3 – The state q2 generates output 0 and transitions to q1 on input ‘0’, and transitions to itself on input ‘1’.
For example, consider the binary number 1011.
Input
| Input | 1 | 0 | 1 | 1 | |
|---|---|---|---|---|---|
| State | q0 | q2 | q1 | q2 | q2 |
| Output | 0 | 0 | 1 | 0 | 0 |
The transition table is as follows β
What is Mealy Machine?
A Mealy machine is a machine in the theory of computation in which the output symbol is linked to the transition (state and input) of a finite state machine.
The present input symbol and present state of the machine determine the output symbol in a Mealy machine.
To represent the output in the Mealy machine, each input symbol is associated with an output and separated by a slash for each state.
We can describe the Mealy machine with six tuples (Q, q0, Ξ£, O, Ξ΄, Ξ»’)
where:
- Q is a finite set of states.
- q0 is the initial state.
- Ξ£ is a finite set of input alphabet.
- O is the output alphabet.
- Ξ΄ is the transition function where Q Γ Ξ£ β Q.
- Ξ»’ is the output function where Q Γ Ξ£ β O.
Example 2
Input β 11
Output β 00
The transition diagram is as follows β
Explanation:
- Step 1 – When we input β0β, the start state q0 transitions to state b and generates an output β0β. When we input β1β, q0 transitions to state q2 and generates an output β0β.
- Step 2 – When we input β0β, q1 transitions to itself and generates an output β0β. When we input β1β, q1 transitions to q2 and generates an output β1β.
- Step 3 – When we input β1β, q2 transitions to itself and generates an output β0β. When we input β0β, q2 transitions to state q1 and generates an output β1β.
The transition state table of a Mealy Machine is β
Characteristics of Mealy and Moore Machine:
Below given are the Characteristics of Mealy and Moore Machine-
Characteristics of Mealy Machine:
- A Mealy machine has lesser states than a Moore machine.
- It changes its output based on its present state and current input, and places the output on the transition.
- Mealy machines react to inputs faster than other machines, within the same clock cycle.
- When the input logic is done in the present state, the value of the output function becomes a function of transitions and changes.
- Designing a Mealy machine generally requires very few states, and the asynchronous generation of output through its state alters to synchronous on the present clock.
- The process of designing a Mealy machine requires little hardware, but it is not necessarily easy.
Characteristics of Moore Machine:
- A Moore Machine has more states than the Mealy Machine.
- The output of a Moore Machine depends only on its current state and is placed on the transition.
- Whenever the state changes, the output function’s value becomes a function of the current state and the changes at the edges of the clock.
- Both the state and output change synchronously with the clock edge.
- Designing a Moore Machine requires more hardware and more logic for decoding the output. This can lead to more delays in the circuit, which generally react after one clock cycle.
- Additionally, the states required for synthesis in a Moore Machine are also more.
- However, designing a Moore Machine is very easy. You can refer to a counter as a Moore Machine.
Difference between Mealy Machine and Moore Machine
The main difference between Mealy machine and Moore machine is in how they decide their outputs. Mealy machine theory of computation considers both the current state and inputs to make output decisions, while Moore machine theory of computation only considers the current state.
Letβs discuss the difference in the form of a table.
| Mealy Machine | Moore Machine |
|---|---|
| For the same functions’ implementation, this machine requires fewer states. | This machine implements the same functions with a more significant number of states. |
| Designing this machine as a Mealy machine isn’t straightforward. | This is comparatively very easy to design Moore’s machine. |
| These machines respond to changes more quickly and all move in the same direction. | These machines usually react after one clock cycle, and decoding the output requires more logic, resulting in longer circuit delays. |
| Less hardware is required for design by this machine. | More hardware is required for design by this machine. |
| A counter can not be referred | Counter can be referred |
| When you create the input logic in the present state, transitions and changes make the output values a function.. | Every time a change occurs in the state, the output value becomes a function of its current state and the changes at the edges of the clock. |
Conclusion:
In conclusion, the differentiation between Mealy and Moore machines is pivotal in understanding the behavior of finite state machines. Mealy machines, with their output dependence on both current states and inputs, offer flexibility in capturing dynamic relationships. On the other hand, Moore machines simplify the model by tying outputs solely to the current state. The choice between these models depends on the specific requirements of a given application, considering factors such as timing, complexity, and ease of implementation. Whether designing control circuits or pattern recognition systems, grasping the nuances of Mealy and Moore machines is essential for engineers navigating the intricacies of digital system design.
FAQs related to the Difference between Mealy and Moore Machine
Here are some of the FAQs related to Difference between Mealy and Moore Machine:
Q1: What is the key difference between Mealy and Moore machines?
A1: The primary difference lies in how they handle outputs. In Mealy machines, outputs depend on both the current state and the input, while in Moore machines, outputs are determined solely by the current state.
Q2: When would one choose a Mealy machine over a Moore machine, and vice versa?
A2: The choice between Mealy and Moore machines depends on the specific requirements of the application. Mealy machines are often chosen when a system needs to respond quickly to input changes, while Moore machines are preferred for applications where output stability is crucial.
Q3: How do Mealy and Moore machines impact circuit complexity?
A3: Mealy machines can lead to more complex circuits due to their output dependence on both state and input. Moore machines, by tying outputs solely to the state, may result in simpler circuits. The choice depends on the trade-offs between complexity and desired system behavior.
Q4: Can a Mealy machine be converted into a Moore machine, and vice versa?
A4: Yes, it is possible to convert a Mealy machine into a Moore machine and vice versa. The conversion involves adjusting the output logic to reflect the desired behavior while maintaining the state transitions.
Q5: Are Mealy or Moore machines more commonly used in practice?
A5: Both Mealy and Moore machines find practical applications, and the choice depends on the specific requirements of the system being designed. Mealy machines are often used in systems requiring more dynamic responses, while Moore machines are employed in situations where output stability is critical.