Lec3

1. 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.

2. Analysis: Example 1 - State Machine
Analyze 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.
X
Z
Q D
Q Clk

3. Combinational
Logic
Input
Output
X
Z
Excitation
Q D
Present Next State
State Q Clk
Clock
Memory
1. Determine the excitation equations for the flip flop inputs
D = X ⊕Q

4. 2. Substitute the excitation equations into the flip flop
characteristic equations to obtain transition
equations.
Q* = D characteristic equation
Q* = X ⊕ Q transition equation
3. Use transition equations to construct transition table.
Transition table
State Input X
Q 0 1
0 0 1
1 1 0
Next State Q*

5. 4. Determine the output equations.
Z = X ⊕Q 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.
Transition/output table
State Input X
Q 0 1
0 0,0 1,1
1 1,1 0,0
Next State Q*, Z

6. 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 = 1
S is current state & S* is next state.
State/output table
State Input X
S 0 1
A A,0 B,1
B B,1 A,0
Next State S*, Z

7. Draw a state diagram corresponding to the state/output table.
State/output table
State Input X
S 0 1
A A,0 B,1
B B,1 A,0
Next State S*, Z
State diagram
1/1
0/0 A B 0/1
1/0

8. Analysis: Example 2 - State Machine
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9. Analysis: Example 2 - Excitation Equations
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10. Analysis: Example 2 - Transition Equations
• Excitation equations
• Characteristic equations
• Substitute excitation equations into
characteristic equations
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11. Analysis: Ex 2 - Transition/State Tables
transition equations
output equation
transition state table state/output
table table
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12. Analysis: Example 2 - State Diagram
• Mealy machine state diagram
– Circles for states
– Arrows for transitions (note output info)
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