Transcript No Slide Title

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
C H A P T E R
13
Digital Logic Circuits
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.9 Binary and Gray code patterns
for linear position encoders
Decimal
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
McGraw-Hill
Binary
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
Decimal
Gray code
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1000
1001
1011
1010
1110
1111
1101
1100
0100
0101
0111
0110
0010
0011
0001
0000
2
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.10 Binary and Gray code patterns
for angular position encoders
01111
00000 01000
00000
10000
11111 11000
10000
Binary sequence
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Gray code
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.14 Complements and the NOT
gate
X
X
NOT
NOT gate
X
X
1
0
0
1
Truth table for NOT gate
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.17 De Morgan’s laws
=
(X + Y )
X
X
X
Y
OR
NOT
Z
=
AND
NOT
Z
AND
Z
OR
Z
NOT
X +Y
X
X
NOT
=
Y
( X .Y )
. Y
NOT
=
Y
Y
McGraw-Hill
NOT
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.18 Sum-of-products and productof-sum logic functions
A
X
OR
AND
B
Y
OR
( X .Y ) + (W.Z)
(A +B) . (C +D)
C
W
Z
AND
OR
AND
D
Sum of products
expression
( X.Y ) + (W.Z)
McGraw-Hill
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Product of sums
expression
(A +B) . (C+D)
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.21 Equivalence of NAND and
NOR gates with AND and OR gates
A
NAND
B
A
A. B
AND
B
(A . B) = A + B
(A . B)
NOT
A
(A + B) = A . B
NOR
B
A
A+B
OR
B
(A + B)
A
B
A
B
(A . B)
A
B
A
B
(A + B)
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
NAND gate
McGraw-Hill
NOT
NOR gate
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.27 XOR gate
X
XOR
Y
Z=X
X
Y
Z
0
0
0
0
1
1
0
1
1
1
1
0
Y
Truth table
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.28 Realization of an XOR gate
X
OR
Y
AND
Z
NAND
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.30 Truth table and karnaugh map
representations of a logic function
XY
XY
XY
XY
Z
0
1
1
0
Z
0
1
1
0
Karnaugh map
X
Y
Z
Desired
Function
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
Truth table
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.31 Karnaugh map for a fourvariable expression
X
Y
Y
Z
Desired
Function
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
W.X
W.X
W .X
W.X
Y.Z
1
0
0
0
Y.Z
1
1
0
1
Y.Z
0
0
1
0
Y.Z
0
1
0
1
Truth table for four-variable expression
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.55 4-to-1 MUX
Enable
D
Data
inputs
D
D
D
E
0
4-to-1
MUX
1
2
3
F
F
Output
I1
I0
Data select
block diagram of
4-to-1 MUX
I
1
I
F
0
0
0
D
0
1
D
1
1
0
D
2
1
1
D
3
0
Truth table of
4-to-1 MUX
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 13.58 Read-only memory
ROM
address
I
I
1
ROM content
(4-bit words)
0
b
3
b
b
2
1
b
0
0
0
0
1
1
0
W
0
0
1
1
0
0
1
W
1
1
0
0
1
1
0
W
2
1
1
1
1
1
1
W
3
I0
I1
Address
lines
b0
22
4
b1
ROM
b2
E
b3
Wi = output word
Enable
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000