Mealy and Moore Model Machines: State Table and Transition Diagram

Introduction

In CMOS design, Mealy and Moore model machines play a crucial role. These models are used to design sequential circuits and describe the behavior of digital systems. The state table and transition diagram are essential components of these models, providing a visual representation of the circuit's states and transitions.

Mealy Model

The Mealy model is a type of finite state machine that defines the output based on both the current state and the input. It is named after George H. Mealy, who introduced this model in 1955. Unlike the Moore model, the Mealy model's output is not solely determined by the current state.

State Table

The state table is a tabular representation of the Mealy model's states, inputs, outputs, and next states. It helps in understanding the behavior of the circuit and designing the sequential logic. The state table consists of rows representing each state and columns representing inputs, outputs, and next states.

Construction of State Table for Mealy Model

To construct a state table for the Mealy model, follow these steps:

1. Identify the states of the system.
2. Determine the inputs and outputs for each state.
3. Define the next state for each combination of the current state and input.

Example of Constructing a State Table

Consider a vending machine that dispenses a product when a certain amount of money is inserted. The Mealy model state table for this vending machine would include states such as 'Idle,' 'Accepting Money,' 'Dispensing,' and 'Change Given.' The inputs would be the amount of money inserted, and the outputs would be whether the product is dispensed and the change given.

Transition Diagram

The transition diagram is a graphical representation of the Mealy model's states and transitions. It consists of nodes representing states and directed edges representing transitions between states. Each edge is labeled with the input and output associated with that transition.

Construction of Transition Diagram for Mealy Model

To construct a transition diagram for the Mealy model, follow these steps:

1. Identify the states of the system and represent them as nodes.
2. Determine the inputs and outputs for each transition.
3. Draw directed edges between the nodes, labeling them with the input and output.

Example of Constructing a Transition Diagram

Using the vending machine example, the transition diagram would have nodes representing the states and directed edges labeled with the inputs and outputs associated with each transition.

Moore Model

The Moore model is another type of finite state machine that defines the output solely based on the current state. It is named after Edward F. Moore, who introduced this model in 1956. Unlike the Mealy model, the Moore model's output is not influenced by the input.

State Table

The state table for the Moore model is similar to that of the Mealy model, representing the states, inputs, outputs, and next states. However, in the Moore model, the outputs are determined solely by the current state.

Construction of State Table for Moore Model

To construct a state table for the Moore model, follow these steps:

1. Identify the states of the system.
2. Determine the outputs for each state.
3. Define the next state for each combination of the current state and input.

Example of Constructing a State Table

Continuing with the vending machine example, the Moore model state table would include states such as 'Idle,' 'Accepting Money,' 'Dispensing,' and 'Change Given.' The outputs would be whether the product is dispensed and the change given.

Transition Diagram

The transition diagram for the Moore model is similar to that of the Mealy model, representing the states and transitions. However, the transitions in the Moore model are not labeled with inputs and outputs.

Construction of Transition Diagram for Moore Model

To construct a transition diagram for the Moore model, follow these steps:

1. Identify the states of the system and represent them as nodes.
2. Draw directed edges between the nodes, representing the transitions.

Example of Constructing a Transition Diagram

Using the vending machine example, the transition diagram for the Moore model would have nodes representing the states and directed edges representing the transitions.

Comparison between Mealy and Moore Models

There are several differences between the construction of state tables and transition diagrams for the Mealy and Moore models:

• In the Mealy model, the outputs are determined by both the current state and the input, whereas in the Moore model, the outputs are solely determined by the current state.
• The state table for the Mealy model includes columns for inputs, outputs, and next states, while the state table for the Moore model only includes columns for outputs and next states.
• The transition diagram for the Mealy model includes labels for inputs and outputs on the edges, whereas the transition diagram for the Moore model does not include these labels.

In terms of advantages and disadvantages, the Mealy model allows for more flexibility in defining the outputs, as they can be influenced by both the current state and the input. However, this can also lead to more complex designs. The Moore model, on the other hand, simplifies the design process by solely relying on the current state for determining the outputs.

Real-World Applications

The Mealy and Moore models find applications in various real-world scenarios:

• Mealy Model Applications:

  • Traffic light control systems
  • Communication protocols
  • Data encryption algorithms

• Moore Model Applications:

  • Elevator control systems
  • Alarm systems
  • Digital clocks

Conclusion

In conclusion, Mealy and Moore model machines are essential in CMOS design for designing sequential circuits. The state table and transition diagram provide a visual representation of the circuit's behavior and aid in the design process. Understanding the differences between the Mealy and Moore models, as well as their applications, is crucial for successful circuit design in various real-world scenarios.

Summary

Mealy and Moore model machines are important in CMOS design for designing sequential circuits. The Mealy model defines the output based on both the current state and the input, while the Moore model defines the output solely based on the current state. The state table and transition diagram are essential components of these models, providing a visual representation of the circuit's states and transitions. The state table includes the states, inputs, outputs, and next states, while the transition diagram represents the states and transitions. The Mealy model allows for more flexibility in defining the outputs, while the Moore model simplifies the design process by solely relying on the current state. These models find applications in various real-world scenarios such as traffic light control systems, communication protocols, elevator control systems, and alarm systems.

Analogy

Imagine you are playing a video game where you control a character. In the Mealy model, the character's actions and abilities depend not only on their current state but also on the input from the game controller. For example, pressing the jump button while the character is on the ground will make them jump. In the Moore model, the character's actions and abilities are solely determined by their current state. For example, if the character is in a flying state, they can fly regardless of any input from the game controller.