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Chapter 9
9.1. The nextstate and output expressions for the circuit in Figure P9.1 are
Y
1
=
w
1
+
y
1
y
2
Y
2
=
w
2
+
y
1
+
w
1
y
2
z
1
=
y
1
z
2
=
y
2
This gives the excitation table
Present
Next state
state
w
2
w
1
= 00
01
10
11
z
2
z
1
y
2
y
1
Y
2
Y
1
A
00
11
10
11
10
11
B
01
11
11
0
1
0
1
10
C
10
11
1
0
11
1
0
01
D
11
1
1
10
01
10
00
The resulting ±ow table is
Present
Next state
state
w
2
w
1
= 00
01
10
11
z
2
z
1
A
D
C
D
C
11
B
D
D
B
B
10
C
D
C
D
C
01
D
D
C
B
C
00
The behavior is the same as described in the ±ow table in Figure 9.21
a
, if the state interchanges A
↔
D and B
↔
C are made.
91
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View Full Document 9.2. The waveforms are
1
Δ
2
Δ
3
Δ
2
Δ
1
Δ
2
Δ
3
Δ
2
Δ
c
z
1
z
2
The Fow table is
Present
Next state
Outputs,
z
2
z
1
state
C
= 0
1
0
1
0
1
0
00
10
1
1
0
01
00
The circuit generates a nonoverlapping 2phase clock.
9.3. The partitioning procedure gives
P
1
=
(
ADGJMPT
)(
BEHR
)(
CF
)(
ILOSV
)(
KNU
)
P
2
=
(
AD
)(
GP
)(
JMT
)(
B
)(
E
)(
HR
)(
C
)(
F
)(
ILOSV
)(
KNU
)
P
3
=
(
A
)(
D
)(
GP
)(
JMT
)(
B
)(
E
)(
HR
)(
C
)(
F
)(
ILOSV
)(
KNU
)
P
4
=
P
3
This gives the Fow table
Present
Next state
state
w
2
w
1
= 00
01
10
11
z
A
A
B
C

0
B
D
B


0
C
G

C

0
D
D
E
F

0
E
G
E


0
F
J

F

0
G
G
H
I

0
H
J
H


0
I
A

I

1
J
J
K
I

0
K
A
K


1
92
The corresponding merger diagram is
E
D
A
B
C
G
J
I
H
F
K
This leads to the reduced fow table
Present
Next state
state
w
2
w
1
= 00
01
10
11
z
A
A
B
C

0
B
D
B


0
C
G
C
C

0
D
D
C
F

0
F
J
F
F

0
G
G
F
I

0
I
A
I
I

1
J
J
I
I

0
9.4. The partitioning procedure gives
P
1
=
(
AF
)(
BEGL
)(
CJ
)(
DK
)(
HM
)
P
2
=
(
AF
)(
BG
)(
EL
)(
CJ
)(
DK
)(
HM
)
P
3
=
(
A
)(
F
)(
BG
)(
EL
)(
CJ
)(
DK
)(
HM
)
P
4
=
P
3
93
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View Full Document Replacing states
B
and
G
,
E
and
L
,
C
and
J
,
D
and
K
, and
H
and
M
with new states
B
,
E
,
C
,
D
, and
H
,
respectively, produces the following Fow table:
Present
Next state
Output
state
w
2
w
1
= 00
01
10
11
z
A
A
B
C

0
B
D
B

H
0
C
F

C
H
0
D
D
E
C

1
E
A
E

H
0
F
F
E
C

0
H

B
C
H
1
The merger diagram is
A
H
B
C
F
D
E
Only
C
and
F
can be merged if the Moore model is to be preserved. Therefore, the reduced Fow table is
Present
Next state
state
w
2
w
1
= 00
01
10
11
z
A
A
B
C

0
B
D
B

H
0
C
C
E
C
H
0
D
D
E
C

1
E
A
E

H
0
H

B
C
H
1
94
9.5. Relabel the fow table as
Present
Next state
Output
z
state
w
2
w
1
= 00
01
10
11
00
01
10
11
A
1
3
7
2
0

1
1
B
5
3
4
8
0
1
0
0
C
5
6
4
2
0
1
0
1
D
1
6
7
8


1
0
The transition diagram is
D
A
B
3
1 7
,
4 5
,
C
2
8
6
The diagonal transitions cannot be avoided without introducing additional states. A possible modiFcation is
D
A
B
3
1 7
,
4 5
,
C
2
8
6
4 5
,
G
8
F
6
E
This transition diagram can be embedded onto a 3cube as ±ollows:
D
A
B
F
G
C
E
8
6
3
4 5
,
1 7
,
8
y
2
y
3
y
1
2
6
4 5
,
95
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This note was uploaded on 02/16/2011 for the course EE 4745 taught by Professor Rai during the Spring '07 term at LSU.
 Spring '07
 Rai

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