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What must be true for the OR of all conditions of transitions leaving a state?
What must be true for the OR of all conditions of transitions leaving a state?
Which expression is equivalent to $a + a'b$?
Which expression is equivalent to $a + a'b$?
In the context of transition conditions, what does it indicate if the AND of each pair is always 0?
In the context of transition conditions, what does it indicate if the AND of each pair is always 0?
What is the result of the expression $ab' * (a'b' + a'b + ab)$?
What is the result of the expression $ab' * (a'b' + a'b + ab)$?
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Which of the following describes a property that must be obeyed by transitions in a finite state machine?
Which of the following describes a property that must be obeyed by transitions in a finite state machine?
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What does the equation $ar * a' * a(r' + b + g)$ simplify to?
What does the equation $ar * a' * a(r' + b + g)$ simplify to?
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In the given transitions, which button presses are intuitively represented by $ar * a(r' + b + g)$?
In the given transitions, which button presses are intuitively represented by $ar * a(r' + b + g)$?
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How can you state a transition could be true in the context provided?
How can you state a transition could be true in the context provided?
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Which flip-flop type is noted for use in this course?
Which flip-flop type is noted for use in this course?
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What is one of the first steps in the design process using FSMs?
What is one of the first steps in the design process using FSMs?
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In the equation $ar(r' + b + g)$, what does it indicate if a transition fails?
In the equation $ar(r' + b + g)$, what does it indicate if a transition fails?
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What does the note about the author imply regarding the pitfall mentioned?
What does the note about the author imply regarding the pitfall mentioned?
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In the equation $0 + arb + arg$, what happens to the transitions when the output is zero?
In the equation $0 + arb + arg$, what happens to the transitions when the output is zero?
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What is the primary function of the described synchronous sequential machine?
What is the primary function of the described synchronous sequential machine?
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Which model is used to represent the machine that outputs based on current and previous states?
Which model is used to represent the machine that outputs based on current and previous states?
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In the state transition table of the Mealy model, what is the output when in state 4 and the input is 10?
In the state transition table of the Mealy model, what is the output when in state 4 and the input is 10?
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How many unique states are defined in the Moore model's state transition table?
How many unique states are defined in the Moore model's state transition table?
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What happens to redundant states in the state diagram of the machine?
What happens to redundant states in the state diagram of the machine?
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Which state does the machine transition to when in state 3 with inputs 11 in the Moore model?
Which state does the machine transition to when in state 3 with inputs 11 in the Moore model?
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Which input pair results in the machine outputting 1 in the Mealy model?
Which input pair results in the machine outputting 1 in the Mealy model?
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What is the output for the input pair 00 in state 2 of the Mealy model?
What is the output for the input pair 00 in state 2 of the Mealy model?
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What happens when the finite state machine enters an unused state?
What happens when the finite state machine enters an unused state?
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What is the state of the finite state machine when U=0?
What is the state of the finite state machine when U=0?
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Which of the following represents the unused states in the modulo 6 counter?
Which of the following represents the unused states in the modulo 6 counter?
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What should be done with the unused states to handle them effectively?
What should be done with the unused states to handle them effectively?
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What indicates that the machine is in an invalid state?
What indicates that the machine is in an invalid state?
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In the revised modulo 6 counter diagram, what happens when the present state is 110?
In the revised modulo 6 counter diagram, what happens when the present state is 110?
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What is a condition that leads to the FSM being in an unused state upon power-up?
What is a condition that leads to the FSM being in an unused state upon power-up?
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What is a key aspect of the transition from an unused state to a valid state in the modulo 6 counter?
What is a key aspect of the transition from an unused state to a valid state in the modulo 6 counter?
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What is a key characteristic of Mealy machines?
What is a key characteristic of Mealy machines?
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What advantage do Moore machines have over Mealy machines?
What advantage do Moore machines have over Mealy machines?
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What must occur to eliminate glitches in a Mealy machine?
What must occur to eliminate glitches in a Mealy machine?
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In the context of the FSM example for a secure car key, what triggers the transmission of the ID?
In the context of the FSM example for a secure car key, what triggers the transmission of the ID?
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What is the output value 'r' during the 'Wait' state in the secure car key FSM?
What is the output value 'r' during the 'Wait' state in the secure car key FSM?
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What happens if an incorrect button is pressed in the FSM for the code detector?
What happens if an incorrect button is pressed in the FSM for the code detector?
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In what order must the buttons be pressed in the code detector FSM?
In what order must the buttons be pressed in the code detector FSM?
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Why might some designers prefer using Mealy machines?
Why might some designers prefer using Mealy machines?
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What is the output 'u' of the FSM in the code detector when the sequence is completed successfully?
What is the output 'u' of the FSM in the code detector when the sequence is completed successfully?
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Which of the following best describes how synchronization is achieved in Mealy machines?
Which of the following best describes how synchronization is achieved in Mealy machines?
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Which FSM state indicates that no button has been pressed yet in the code detector?
Which FSM state indicates that no button has been pressed yet in the code detector?
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How does the output of the Mealy machine compare to that of the Moore machine?
How does the output of the Mealy machine compare to that of the Moore machine?
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What is the purpose of timing diagrams in FSM designs?
What is the purpose of timing diagrams in FSM designs?
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Which state must be reached after the 'Start' state in the code detector FSM?
Which state must be reached after the 'Start' state in the code detector FSM?
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The Moore model's outputs are dependent on the current input variables.
The Moore model's outputs are dependent on the current input variables.
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Mealy machines tend to require more states than Moore machines due to their output functions being dependent on both state and input.
Mealy machines tend to require more states than Moore machines due to their output functions being dependent on both state and input.
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In the Moore model, outputs change asynchronously with state transitions and clock edges.
In the Moore model, outputs change asynchronously with state transitions and clock edges.
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The output functions of the Moore machine are simpler than those of the Mealy machine, as they are based solely on states.
The output functions of the Moore machine are simpler than those of the Mealy machine, as they are based solely on states.
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Both Mealy and Moore machines use the same state diagram structure for illustrating their functionality.
Both Mealy and Moore machines use the same state diagram structure for illustrating their functionality.
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The Mealy model provides outputs that are triggered based on the state transition process.
The Mealy model provides outputs that are triggered based on the state transition process.
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Transitions in a Moore machine are labeled with output conditions instead of input combinations.
Transitions in a Moore machine are labeled with output conditions instead of input combinations.
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A Mealy machine's outputs can change immediately with changes in input conditions while in the same state.
A Mealy machine's outputs can change immediately with changes in input conditions while in the same state.
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The unused states for the modulo 6 counter are 110 and 111.
The unused states for the modulo 6 counter are 110 and 111.
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Whenever U=1, the state counter will always increment.
Whenever U=1, the state counter will always increment.
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The modulo 6 counter can enter an invalid state upon power-up.
The modulo 6 counter can enter an invalid state upon power-up.
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Creating dummy states can help ensure the FSM transitions to known states.
Creating dummy states can help ensure the FSM transitions to known states.
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If the current state is 111 and U=1, the next state will also be 111.
If the current state is 111 and U=1, the next state will also be 111.
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A state diagram specifies all transitions for every possible input combination.
A state diagram specifies all transitions for every possible input combination.
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The output value C=0 indicates the FSM is in a valid state.
The output value C=0 indicates the FSM is in a valid state.
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Incrementing the counter when the state is 101 leads to the desired state of 000.
Incrementing the counter when the state is 101 leads to the desired state of 000.
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Mealy machines have a synchronous design methodology.
Mealy machines have a synchronous design methodology.
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Moore machines are known for producing glitch-free outputs.
Moore machines are known for producing glitch-free outputs.
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To convert a Mealy machine to a Moore machine, synchronization is required.
To convert a Mealy machine to a Moore machine, synchronization is required.
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The outputs of Mealy machines can change in response to input changes regardless of the clock.
The outputs of Mealy machines can change in response to input changes regardless of the clock.
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A code detector FSM opens the door when any button is pressed.
A code detector FSM opens the door when any button is pressed.
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In a synchronous Mealy machine, every output is dependent on the current state and inputs.
In a synchronous Mealy machine, every output is dependent on the current state and inputs.
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The secure car key FSM transmits its identifier when the computer requests it.
The secure car key FSM transmits its identifier when the computer requests it.
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If an incorrect button is pressed in the code detector FSM, the sequence is terminated.
If an incorrect button is pressed in the code detector FSM, the sequence is terminated.
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The input identifier transmitted by the secure car key FSM is always a 4-bit number.
The input identifier transmitted by the secure car key FSM is always a 4-bit number.
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If a Mealy machine is modified to eliminate glitches, it remains a Mealy machine.
If a Mealy machine is modified to eliminate glitches, it remains a Mealy machine.
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The start button is a critical input in the FSM for the code detector.
The start button is a critical input in the FSM for the code detector.
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Synchronous Mealy machines do not require clock signals for their operation.
Synchronous Mealy machines do not require clock signals for their operation.
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Moore machines tend to have more states compared to Mealy machines.
Moore machines tend to have more states compared to Mealy machines.
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Outputs of a FSM depend on both its current state and previous inputs.
Outputs of a FSM depend on both its current state and previous inputs.
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A modulo 6 counter uses the binary value 110 in its counting sequence.
A modulo 6 counter uses the binary value 110 in its counting sequence.
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In a Moore machine, the outputs are generated solely from the current state.
In a Moore machine, the outputs are generated solely from the current state.
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When the input U is set to 0, the modulo 6 counter increments its value.
When the input U is set to 0, the modulo 6 counter increments its value.
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The value of the modulo 6 counter is represented as a 2-bit value.
The value of the modulo 6 counter is represented as a 2-bit value.
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A Moore model outputs based solely on the current state of the machine.
A Moore model outputs based solely on the current state of the machine.
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The output C of the modulo 6 counter is 1 when the counter transitions from state 5 to state 0.
The output C of the modulo 6 counter is 1 when the counter transitions from state 5 to state 0.
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In a finite state machine's state transition table, each present state can have multiple outputs for a given pair of inputs.
In a finite state machine's state transition table, each present state can have multiple outputs for a given pair of inputs.
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A decoder generates the next state logic for the modulo 6 counter.
A decoder generates the next state logic for the modulo 6 counter.
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In a Mealy machine, the outputs are influenced by both the state and the system inputs.
In a Mealy machine, the outputs are influenced by both the state and the system inputs.
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The combination of inputs 00 and 10 in state 2 of the Mealy model results in an output of 1.
The combination of inputs 00 and 10 in state 2 of the Mealy model results in an output of 1.
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Redundant states in a state diagram should be removed for efficient implementation of a sequential machine.
Redundant states in a state diagram should be removed for efficient implementation of a sequential machine.
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The output value of a modulo 6 counter is always 0 to 5.
The output value of a modulo 6 counter is always 0 to 5.
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The next state of the modulo 6 counter can only be generated when U is set to 1.
The next state of the modulo 6 counter can only be generated when U is set to 1.
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The output of the Moore machine for state 5 and inputs 01 is 1.
The output of the Moore machine for state 5 and inputs 01 is 1.
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The transition conditions for the modulo 6 counter involve examining all possible input values.
The transition conditions for the modulo 6 counter involve examining all possible input values.
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The Mealy model's output is contingent on both the current state and inputs while Moore models rely solely on the inputs.
The Mealy model's output is contingent on both the current state and inputs while Moore models rely solely on the inputs.
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A synchronous sequential machine is designed to detect a specific pattern of input occurrences.
A synchronous sequential machine is designed to detect a specific pattern of input occurrences.
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The state transition from state 1 to state 2 with input 00 produces an output of 1 in the Mealy model.
The state transition from state 1 to state 2 with input 00 produces an output of 1 in the Mealy model.
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Study Notes
Mealy vs Moore Machines
- Mealy machines have asynchronous outputs which change in response to input changes, independent of a clock.
- Moore machines have a more disciplined timing methodology than Mealy machines due to their synchronous outputs.
- Traditionally, Mealy models are used for synchronous design, and Moore models are used for asynchronous design.
- Mealy machines can have glitches in their outputs due to their asynchronous nature.
- Some designers prefer Mealy machines because they can result in fewer states compared to Moore machines.
- Moore machines have glitch-free outputs.
- To eliminate glitches in a Mealy machine, its output needs to be synchronized, effectively transforming it into a Moore machine.
Synchronous Mealy Machines
- Synchronizing a Mealy machine involves breaking the direct connection between inputs and outputs by introducing storage elements.
- Storage elements act as a buffer, allowing the system to respond to changes only at designated points.
- The clock signal drives the state register and the combinatorial logic responsible for output and next-state determination.
FSM Example: Secure Car Key
- Many new car keys incorporate tiny computer chips.
- When starting the car, the car's computer (under the hood) requests an identifier from the key.
- The key transmits its identifier to the computer in a specific sequence, one bit at a time, using a Finite State Machine (FSM).
- The FSM has a set of states (Wait, K1, K2, K3, K4) and responds to the input (a).
- If the identifier is incorrect, the computer shuts off the car.
FSM Example: Code Detector
- The FSM example is a code detector which unlocks a door only when buttons are pressed in a specific sequence: start, red, blue, green, red.
- The FSM waits for the "start" button (s=1) before transitioning to the "start" state.
- It then progresses to the "red", "blue", "green", and "red" states in sequence.
- Each state corresponds to pressing a specific coloured button.
- The FSM uses input signals (s, r, g, b) representing each button and output signal (a) indicating when a coloured button is pressed.
- If the correct sequence is followed, the door unlocks (u=1).
- If an incorrect button is pressed at any step, the FSM returns to the "Wait" state without unlocking the door.
State Reduction
- State tables and diagrams may contain redundant states that can be eliminated to reduce the number of components needed for implementation.
- Removing redundant states streamlines the design by reducing the overall complexity.
Unused States
- If a finite state machine enters an unused state, a problem can occur with the FSM's functionality.
- Unused states, also known as unknown or undefined states, can arise from design flaws or power-up situations.
- Unused states can be handled by creating dummy states that transition to a known state on the next clock cycle.
Modulo 6 Counter Analysis
- A modulo 6 counter has six states with binary values from 000 to 101.
- The counter's state is stored in the state register of the finite state machine's hardware.
- Unused states, such as 110 and 111, are not intended to be accessed and can cause unpredictable behavior.
- To handle unused states in the modulo 6 counter, dummy states 110 and 111 are created and transition to a known state on the next clock cycle. This ensures that the finite state machine always remains in a valid state.
FSM Design Process
- Determine the information to be stored in the FSM's memory.
- Encode the inputs and outputs in binary representation, if necessary.
- Construct a state diagram to represent the desired behavior of the device.
- Assign a binary number (code) to each state.
- Choose the type of flip-flop to use.
- Derive the flip-flop input maps.
- Create the combinational logic equations and draw the schematic based on the equations.
Mealy Machine
- Outputs are associated with transitions between states, labeled with both input combinations and output values
- Example: "00/0" represents an input of "00" resulting in an output of "0"
- Changes in output value occur asynchronously when inputs change, independent of the clock cycle
Moore Machine
- Outputs are associated with specific states, labeled with state names
- Outputs change synchronously with state transitions with a clock edge
- Example: A state named "C" could have an output value of "0", independent of input changes
Moore vs Mealy
- Moore machines use a larger number of states to manage output conditions, resulting in simpler output function logic that is independent of input variables
- Mealy machines typically require fewer states, but their asynchronous output behavior can lead to glitches
- For synchronous design, Mealy machines are common; Moore machines are used for asynchronous design
Synchronous Moore Machine
- Mealy machines are often synchronized to eliminate glitches.
- The Mealy machine output is connected to storage elements (like flip-flops) with an active clock signal to ensure output synchronization.
- Essentially converting the Mealy machine into a Moore machine.
Car Key Secure FSM
- Small computer chips in car keys function as finite state machines.
- The car's computer requests an identifier from the key during startup.
- The key transmits a 4-bit identifier bit-by-bit.
- If the identifier matches, the startup sequence completes; if not, the engine shuts off.
Code Detector FSM
- Designed to unlock a door (u=1) by a specific sequence of button presses: "start", "red", "blue", "green", "red".
- Inputs are: "s" for start, "r" for red, "g" for green, "b" for blue, and "a" for button press.
- Outputs are: "u" for unlock and "a" for button press indication.
- The FSM starts in a "Wait" state.
- An incorrect button sequence results in returning to the "Wait" state and not unlocking the door.
Modulo 6 Counter
- A 3-bit counter that cycles through states 000-101.
- Input "U" controls counting:
- When U=1, the counter increments on the rising edge of the clock.
- When U=0, the counter retains its value.
- Output "C" is 1 for the 101-000 transition, and 0 otherwise.
Modulo 6 Counter State Diagram
- In a Moore machine, outputs are represented alongside each state.
- Inputs are on the arcs connecting the states.
- The state transitions based on the input "U".
FSM with Counter and Decoder
- The counter acts as a register for storing the current state and also contributes to the next state logic.
- The counter output drives a decoder, with each decoder output representing a specific state.
- Combinational logic uses inputs and decoder outputs to generate both system outputs and next-state information.
- A Mealy machine is implemented when inputs are used to direct both the next state and system outputs.
- A Moore machine arises when outputs only rely on the state value, and inputs only control the next state transition.
Unused States in FSMs
- FSMs that are not in a known/valid state are considered to be in an unused state.
- This can occur during power-up or due to design flaws.
- Unused states may prevent the FSM from reaching a valid state.
Handling Unused States in Modulo 6 Counter
- Implement dummy states to handle unused states (like 110 and 111).
- Dummy states transition to a known state on the next clock cycle.
- Outputs from dummy states can be used to indicate an error condition.
State Reduction
- Redundant states in a state table/diagram can be eliminated, reducing the complexity of the implemented circuit and the number of components used.
- Aim is to achieve transitions to the same state from different combinations of input values without always going through the same state.
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Description
This quiz explores the key differences between Mealy and Moore machines, including their output behaviors and synchronization methods. You'll learn about the advantages and disadvantages of each type, as well as the implications for design choices in synchronous and asynchronous environments.
