11.1 FSM Fundamentals and Models
2 min read•july 25, 2024
(FSMs) are crucial tools in digital design, modeling system behavior through , , , and . They help engineers create sequential logic circuits and algorithms by representing complex systems in a structured, easy-to-understand format.
FSMs come in various models, including deterministic, non-deterministic, Mealy, and . These can be visually represented using or tables, making it easier to analyze and implement system behavior in digital circuits and software.
FSM Fundamentals
Components of finite state machines
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- Finite State Machines (FSMs) serve as mathematical models of computation used to design sequential logic circuits and algorithms
- States represent current condition or configuration of system (ON/OFF)
- Inputs act as external stimuli triggering state transitions (button press)
- Transitions define rules for system movement between states
- Outputs produce results or actions in response to inputs and current state (light turning on)
States and transitions in FSMs
- States embody distinct configurations or situations system can occupy represented by circles in state diagrams (idle, processing, error)
- Transitions facilitate movements between states triggered by specific inputs or conditions depicted by arrows in state diagrams
- Inputs function as external signals or events affecting system causing state transitions or producing outputs often labeled on transition arrows (sensor readings, user commands)
FSM Models and Representation
Types of FSM models
- (DFSMs) feature exactly one transition for each possible input in every state ensuring predictable and unambiguous behavior
- (NFSMs) allow multiple transitions for same input in states enabling simultaneous transitions to multiple states
- produce outputs dependent on both current state and input associating output with transitions
- Moore Machines generate outputs based solely on current state linking output to states themselves
Representation of FSM behavior
- State Transition Diagrams provide graphical representation of behavior
- Draw circles representing states
- Connect states with arrows indicating transitions
- Label arrows with input/output pairs
- Mark start state with incoming arrow
- Denote accept states (if applicable) using double circles
- offer tabular representation of FSM behavior
- Columns include current state, input, next state, and output (for Mealy machines)
- Rows encompass all possible state-input combinations
- Example of simple FSM diagram:
- States A and B
- Transitions: A to B (input 1), B to A (input 0), A to A (input 0), B to B (input 1)
Key Terms to Review (18)
Control logic: Control logic refers to the combination of hardware and software that manages the operations of a digital system by dictating the sequence of operations and the flow of data. It ensures that various components work together smoothly by interpreting inputs and generating outputs, acting as the brain of digital circuits like finite state machines and arithmetic logic units. This concept is crucial for enabling complex behaviors in systems, allowing for decision-making processes based on conditional operations.
Deterministic finite state machines: Deterministic finite state machines (DFSMs) are computational models used to represent and control the execution of a system with a limited number of states. In a DFSM, for each state and input symbol, there is exactly one transition to another state, which ensures predictability and consistency in behavior. This model is foundational in understanding how systems can process input sequences and produce outputs based on predefined rules.
Dfsm: A deterministic finite state machine (DFSM) is a computational model used to design algorithms and systems that have a finite number of states, where each state can transition to another based on a given input. In a DFSM, for each state and input combination, there is exactly one possible next state, making it predictable and efficient for tasks like parsing and recognizing patterns. This characteristic allows DFSMs to be utilized in various applications such as compilers, network protocols, and digital circuit design.
Finite State Machines: A finite state machine (FSM) is a computational model used to design algorithms and systems that can be in one of a finite number of states at any given time, with transitions between states based on input signals. FSMs are foundational in digital design, particularly for applications like counters and control logic, allowing for efficient modeling of sequential processes through defined states and transitions.
Fsm: FSM, or Finite State Machine, is a computational model used to design both computer programs and sequential logic circuits. An FSM consists of a finite number of states, transitions between those states, and actions associated with each state or transition, making it a foundational concept in digital design for representing and controlling complex systems.
Input alphabet: The input alphabet is a finite set of symbols that a finite state machine (FSM) can recognize and process as inputs. It serves as the foundation for defining the behavior and transitions within the FSM, allowing it to respond appropriately to different sequences of input symbols. Each symbol in the input alphabet represents a distinct state or action that influences how the FSM operates and transitions between states.
Inputs: Inputs refer to the signals or data received by a system, which influence its behavior and functioning. In the context of finite state machines (FSMs), inputs drive transitions between states, impacting the output behavior of the system. Understanding inputs is crucial as they help determine how a system responds to different conditions, forming the basis for designing reliable and effective digital circuits.
Mealy Machines: A Mealy machine is a type of finite state machine where the output is determined by the current state and the current input. This model contrasts with Moore machines, where the output depends only on the current state. In Mealy machines, outputs can change as soon as the inputs change, making them more responsive and often more efficient in terms of the number of states required to represent certain behaviors.
Moore Machines: Moore machines are a type of finite state machine (FSM) characterized by their output being solely determined by the current state, rather than the input. This means that the output is stable and only changes upon entering a new state, which can provide advantages in certain design scenarios. Moore machines are often used in digital design due to their predictable behavior, making them suitable for applications requiring reliable state transitions.
NFSM: NFSM stands for Non-deterministic Finite State Machine, a computational model that represents a finite number of states, transitions between those states, and accepts or rejects input strings based on its defined rules. In an NFSM, for a given input and current state, the machine may transition to one or more possible next states, allowing for multiple possible paths through the state space. This non-determinism differentiates NFSM from deterministic finite state machines (DFSM), where each state has exactly one transition for each input symbol.
Non-deterministic finite state machines: Non-deterministic finite state machines (NFSMs) are computational models that can be in multiple states at the same time for a given input. Unlike deterministic finite state machines (DFSMs), which have a single possible next state for each input, NFSMs allow for multiple transitions from one state to another for the same input symbol, enabling a more flexible and complex representation of computational processes.
Output function: The output function is a crucial component in finite state machines (FSMs) that determines the output values based on the current state and possibly the input signals. This function plays a significant role in defining how the system behaves, as it maps states to outputs, which can either be directly related to the inputs or depend solely on the state itself. Understanding this function is essential for designing systems that respond correctly to various input conditions.
Outputs: Outputs refer to the signals or information produced by a system in response to inputs and the current state. In digital design, outputs are crucial as they determine how a system behaves and interacts with the outside world based on its internal processing. These outputs can be either direct responses to inputs or influenced by the internal state of the system, making them essential for understanding how systems operate and react over time.
Protocol design: Protocol design refers to the process of creating a set of rules and conventions that govern communication between different systems or components, ensuring that data is transmitted accurately and efficiently. This concept is crucial in the development of finite state machines (FSMs), where the behavior of the machine is defined by the states it can be in and the transitions triggered by inputs, emphasizing the importance of establishing clear protocols for state changes and data handling.
State transition diagrams: State transition diagrams are visual representations that illustrate how a system transitions from one state to another based on specific inputs or conditions. They provide a clear way to model the behavior of finite state machines (FSMs) by showing states, transitions, and events that trigger those transitions, helping to understand and design complex systems in digital design.
State transition tables: State transition tables are organized charts used to represent the behavior of finite state machines (FSMs), detailing how a system transitions from one state to another based on input events. These tables capture the current state, possible inputs, resulting states, and outputs in a clear and structured manner, making them essential for understanding and designing digital systems. They serve as a visual tool that aids in the design and verification of sequential logic circuits.
States: In the context of digital design, states refer to the distinct conditions or configurations of a system at any given time, especially in finite state machines (FSMs). States define the behavior of the system based on current inputs and determine how the system transitions from one state to another. They are essential for modeling dynamic systems where outputs depend on both current states and inputs.
Transitions: Transitions refer to the change of states in finite state machines (FSMs), which can be visualized as the pathways that connect different states based on input conditions. These pathways are essential for defining how a system reacts to inputs and moves from one state to another. Understanding transitions helps in analyzing the behavior of systems, whether they are simple circuits or complex algorithms, ensuring that the correct outputs are produced as inputs change.