Analysis of state machines
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Detailed steps in the Analysis Process 1. Determine the excitation equations for the flip flop inputs 2. Substitute the excitation equations into the flip flop characteristic equations to obtain transition equations. 3. Use transition equations to construct transition table. 4. Determine the output equations. 5. Add output values to the transition table for each state (Moore) or state /input combination (Mealy) to create a transition/output table. 6. Name the states and substitute state names for state – variable combinations in the transition/output table to obtain the state/output table. 7. Draw a state diagram corresponding to the state/output table.
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Transcript of Analysis of state machines
Detailed steps in the Analysis Process1. Determine the excitation equations for the flip flop inputs
2. Substitute the excitation equations into the flip flop characteristic equations to obtain transition equations.
3. Use transition equations to construct transition table.
4. Determine the output equations.
5. Add output values to the transition table for each state (Moore) or state /input combination (Mealy) to create a transition/output table.
6. Name the states and substitute state names for state – variable combinations in the transition/output table to obtain the state/output table.
7. Draw a state diagram corresponding to the state/output table.
Analysis: Example 1 - State MachineAnalyze the synchronous state machines shown below. Determine the excitation equations, transition equations and output equations. Construct the transition output table and state output table. Draw the state diagram.
DQ
Q
XZ
Clk
DQ
Q
XZ
Clk
InputOutput
Next StatePresent State
CombinationalLogic
MemoryClock
Excitation
1. Determine the excitation equations for the flip flop inputs
QXD
2. Substitute the excitation equations into the flip flop characteristic equations to obtain transition equations.
DQ *
QXQ *
characteristic equation
transition equation
3. Use transition equations to construct transition table.
State Input X
Q 0 1
0 0 1
1 1 0
Next State Q*
Transition table
4. Determine the output equations.
QXZ output equation
5. Add output values to the transition table for each state (Moore) or state /input combination (Mealy) to create a transition/output table.
State Input X
Q 0 1
0 0,0 1,1
1 1,1 0,0
Next State Q*, Z
Transition/output table
6. Name the states and substitute state names for state – variable combinations in the transition/output table to obtain the state/output table.
Substituting state names ‘A’ for state Q = 0 & ‘B’ for state Q = 1S is current state & S* is next state.
State Input X
S 0 1
A A,0 B,1
B B,1 A,0
Next State S*, Z
State/output table
7. Draw a state diagram corresponding to the state/output table.
State Input X
S 0 1
A A,0 B,1
B B,1 A,0
Next State S*, Z
State/output table
State diagram
A B0/0 0/1
1/1
1/0
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Analysis: Example 2 - State Machine
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Analysis: Example 2 - Excitation Equations
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Analysis: Example 2 - Transition Equations
• Excitation equations
• Characteristic equations
• Substitute excitation equations into characteristic equations
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Analysis: Ex 2 - Transition/State Tables
transitiontable
state table state/outputtable
transition equations
output equation
Analysis: Example 2 - State Diagram
• Mealy machine state diagram– Circles for states– Arrows for transitions (note output info)
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