CHAPTER 6 Sequential Circuits’ Analysis

1. CHAPTER 6Sequential 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 I 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 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 Transition Table for state machine M1 • T flip-flop used to realize circuit (two T flip-flops)

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 Transition Table for state machine M1 • J-K flip-flop used to realize circuit (two J-K flip-flops) 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 Cost X Y Z Z= FAFB’xy

26. TO BE CONTINUED