数字逻辑chapter6.1

State Table
A A A B B B B C C C C D D D D
Transition Table
FA FB 0 1 0 1 State A B C D
Each state is assigned a unique code.
0 0 1 1
Transition Table for state machine M1
S-R flip-flop used to realize circuit
Transition Table for state machine M1
S-R flip-flop excitation table Qt 0 0 1 1 Qt+1 0 1 0 1 S 0 1 0 d R d 0 1 0
state machine M1 excitation table using S-R flip-flops
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’
X
State Diagram of Mealy model
0/0 00 0/1 1/0 I/O
01 1/0 11
S1
S2
0/1
0/1 1/0
Reads as: When at state s1 and apply input I, we get output O and proceed to state s2.
TA K-Map
TB 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’
Excitation Table and Equations
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’
D flip-flop excitation table Qt 0 0 1 1 Qt+1 0 1 0 1 D 0 1 0 1
state machine M1 excitation table using D flip-flops
Excitation Table and Equations
DA K-Map
10
1/0

State Diagram of Moore model
I
S1/O1 S2/O2
0/0
00,11 01,10 01,10
1/1
00,11
Reads as: When at state s1 with output O1 and apply input I, we proceed to state s2 with Output O2.
State Table
Transition Table for Table machine M1 State state
Present State FA 0 FB 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 Input X 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 Y 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Next State FA 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 FB 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 Output Z 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
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
Excitation Table and Equations
T flip-flop used to realize circuit
Transition Table for state machine M1
T flip-flop excitation table Qt 0 0 1 1 Qt+1 0 1 0 1 T 0 1 1 0
Excitation Table and Equations
Excitation Realization Cost
JA=FBy KA=FB’xy+x’y’+FBy’ JB=FA’x KB=FAx’
Excitation Realization Cost
SA=FBy
RA=FB’xy+x’y’+FBy’
SB=FA’x RB=FAx’
Excitation Realization Cost
2x=y
State variables states
State Diagram

Graphical representation of a state table. Graph node with label s denotes state s
S

Graph edge with label X denotes transition between two states when input X is applied
CHAPTER 6 Sequential Circuits’ Analysis
Sichuan University Software College
Mealy Vs Moore machines

Mealy model:

Both outputs and next state depend both on primary inputs AND present state. Only next state depends directly on primary inputs AND present state. Outputs depend only on present state.
OUTPUT VARIABLES (O)
Mealy sequential circuit model
INPUT VARIABLES (t) EXCITATION IMPUT LOGIC (f) STATE VARIABLES (E) MEMORY CLK （S） OUTPUT LOGIC （g）
OUTPUT VARIABLES (O)

Moore model:

Mealy Vs Moore machines
Moore sequential circuit model
INPUT VARIABLES (t) EXCITATION IMPUT LOGIC (f) STATE VARIABLES (E) MEMORY CLK （S） OUTPUT LOGIC （g）
State Diagram
State Table

Enumerates the relationship between inputs, outputs, and states of the sequential circuit.
State Table
State Table
State Table
Input Present State A X 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 Y 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Next State A A B B B D B D A C C A A C B D Output Z 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
Transition Table for state machine M1
0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
Excitation Table and Equations
D flip-flop used to realize circuit
Transition Table for state machine M1
State Machine Notation
Impute variable Output variable State variable Excitation variable State State variables and states are related by the expression: