1. Sichuan University Software College
CHAPTER 6 Sequential Circuits’ Analysis
Sichuan University Software College

2. Mealy Vs Moore machines
Mealy model:
Both outputs and next state depend both on primary inputs AND present state.
Moore model:
Only next state depends directly on primary inputs AND present state. Outputs depend only on present state.

3. Mealy Vs Moore machines
Moore sequential circuit model
Mealy sequential circuit model

4. State Machine Notation
Impute variable
Output variable
State variable
Excitation variable
State
State variables and states are related by the expression:
2x=y
State variables
states

5. State Diagram Graphical representation of a state table.
Graph node with label s denotes state s
Graph edge with label X denotes transition between two states when input X is applied S X

6. State Diagram of Mealy model
0/0
1/0
I/O 01 S1 S2 00
0/1
Reads as: When at state s1 and apply
input I, we get output O
and proceed to state s2.
0/1
0/1
1/0 10
1/0 11
1/0

7. State Diagram of Moore model
00,11
S1/O1
S2/O2
01,10
0/0
1/1
Reads as: When at state s1 with output
O1 and apply input I,
we proceed to state s2 with
Output O2.
01,10
00,11

8. State Diagram

9. State Table
Enumerates the relationship between inputs, outputs, and states of the sequential circuit.
State Table

10. State Table
State Table

11. Transition Table Each state is assigned a unique code.
Transition Table for state machine M1

12. Transition Table Transition Table for state machine M1

13. Excitation Table and Equations
D flip-flop used to realize circuit (two D flip-flops)
Transition Table for state machine M1
state machine M1 excitation table using D flip-flops

14. Excitation Table and Equations
DA K-Map
DB K-Map
Z K-Map
DA=f(FA,FB,x,y)=Σ(5,7,10,13,15)=FAFB’xy’+FAx’y+FBy
DB=f(FA,FB,x,y)=Σ(2,3,4,5,6,7,14,15)=FA’FB+FA’x+FBx
Z= f(FA,FB,x,y)=Σ(11)=FAFB’xy

15. Excitation Table and Equations
T flip-flop used to realize circuit (two T flip-flops)
Transition Table for state machine M1

16. Excitation Table and Equations
TB K-Map
TA K-Map
TA=f(FA,FB,x,y)=Σ(5,7,8,11,12,14)=FAFB’xy+FAx’y’+FAFBy’+FA’FBy
TB=f(FA,FB,x,y)=Σ(2,3,12,13)=FA’FB’x+FAFBx’

17. Excitation Table and Equations
S-R flip-flop used to realize circuit (two SR flip-flops)
Transition Table for state machine M1
state machine M1 excitation table using S-R flip-flops

18. Excitation Table and Equations
SA K-Map
RA K-Map
SB K-Map
RB K-Map
SA=f(FA,FB,x,y)=Σ(5,7) +Σd(9,10,13,15) =FBy
RA=f(FA,FB,x,y)=Σ(8,11,12,14) +Σd(0,1,2,3,4,6) =FB’xy+x’y’+FBy’
SB=f(FA,FB,x,y)=Σ(2,3) +Σd(4,5,6,7,14,15) =FA’x
RB=f(FA,FB,x,y)=Σ(12,13) +Σd(0,1,8,9,10,11) =FAx’

19. Excitation Table and Equations
J-K flip-flop used to realize circuit (two J-K flip-flops)
Transition Table for state machine M1
state machine M1 excitation table using J-K flip-flops

20. Excitation Table and Equations
JA K-Map
KA K-Map
JB K-Map
KB K-Map
JA=f(FA,FB,x,y)=Σ(5,7) +Σd(8,9,10,11,12,13,14,15) =FBy
KA=f(FA,FB,x,y)=Σ(8,11,12,14) +Σd(0,1,2,3,4,6,7) =FB’xy+x’y’+FBy’
JB=f(FA,FB,x,y)=Σ(2,3) +Σd(4,5,6,7,12,13,14,15) =FA’x
KB=f(FA,FB,x,y)=Σ(12,13) +Σd(0,1,2,3,8,9,10,11) =FAx’

21. Excitation Realization Cost
JA=FBy
KA=FB’xy+x’y’+FBy’
JB=FA’x
KB=FAx’

22. Excitation Realization Cost
SA=FBy
RA=FB’xy+x’y’+FBy’
SB=FA’x
RB=FAx’

23. Excitation Realization Cost
TA=FAFB’xy+FAx’y’+FAFBy’+FA’FBy
TB=FA’FB’x+FAFBx’

24. Excitation Realization Cost
DA=FAFB’xy’+FAx’y+FBy
DB=FA’FB+FA’x+FBx

25. Excitation Realization CostY Z
Z= FAFB’xy

26. TO BE CONTINUED