ECEN 301Discussion #22 – Combinational Logic1 DateDayClass No. TitleChaptersHW Due date Lab Due...
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ECEN 301 Discussion #22 – Combinational Logic 1 Date Day Clas s No. Title Chapters HW Due date Lab Due date Exam 17 Nov Mon 22 Combinational Logic 13.3 – 13.5 LAB 10 18 Nov Tue 19 Nov Wed 23 Sequential Logic 14.1 20 Nov Thu 21 Nov Fri Recitation HW 9 22 Nov Sat 23 Nov Sun 24 Nov Mon 24 ADC – DAC 15.4 25 Tue Recitation HW 10 Schedule…
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Transcript of ECEN 301Discussion #22 – Combinational Logic1 DateDayClass No. TitleChaptersHW Due date Lab Due...
ECEN 301 Discussion #22 – Combinational Logic 1
Date Day ClassNo.
Title Chapters HWDue date
LabDue date
Exam
17 Nov Mon 22 Combinational Logic 13.3 – 13.5
LAB 1018 Nov Tue
19 Nov Wed 23 Sequential Logic 14.1
20 Nov Thu
21 Nov Fri Recitation HW 9
22 Nov Sat
23 Nov Sun
24 Nov Mon 24 ADC – DAC 15.4
25 Nov Tue Recitation HW 10
Schedule…
ECEN 301 Discussion #22 – Combinational Logic 2
Remember and be Thankful
2 Nephi 1:9, 20: 9 Wherefore, I, Lehi, have obtained a promise, that inasmuch as those whom
the Lord God shall bring out of the land of Jerusalem shall keep his commandments, they shall prosper upon the face of this land; and they shall be kept from all other nations, that they may possess this land unto themselves. And if it so be that they shall keep his commandments they shall be blessed upon the face of this land, and there shall be none to molest them, nor to take away the land of their inheritance; and they shall dwell safely forever.
20 And he hath said that: Inasmuch as ye shall keep my commandments ye shall prosper in the land; but inasmuch as ye will not keep my commandments ye shall be cut off from my presence.
ECEN 301 Discussion #22 – Combinational Logic 3
Lecture 22 – Boolean Algebra & Combinational Logic
ECEN 301 Discussion #22 – Combinational Logic 4
Boolean Algebra
Boolean Algebra: the mathematics associated with binary numbersDeveloped by George Boole in 1854
Variables in boolean algebra can take only one of two possible values:0 → FALSE1 → TRUE
ECEN 301 Discussion #22 – Combinational Logic 5
Rules of Boolean Algebra
ZXYXZXZYYX
YXYXX
ZYXZXYX
XYXX
XZXX
.19
.18
)()(.17
)(.61
.15
XX
XX
XXX
XX
X
XX
XXX
X
XX
.9
0.8
.7
1.6
00.5
1.4
.3
11.2
0.1
ZXYXZYX
ZYXZYX
ZYXZYX
XYYX
XYYX
)(.14
)()(.13
)()(.12
.11
.10
ECEN 301 Discussion #22 – Combinational Logic 6
DeMorgan’s Law
BABA
BABA
To distribute the bar,change the operation.
NOR Symbols
NAND Symbols
ECEN 301 Discussion #22 – Combinational Logic 7
Boolean Algebra
Example1: simplify the following function
ACDBCDBDADBAOUT
ECEN 301 Discussion #22 – Combinational Logic 8
Boolean Algebra
Example1: simplify the following function
CADOUT
DACDOUT
DABCDOUT
BCDCDDAOUT
BCDCADOUT
BCDACADOUT
ACDBCDDAOUT
ACDBCDBBDAOUT
ACDBCDBDADBAOUT
14 Rule
2 Rule)1(
14 Rule
14 Rule
18 Rule
14 Rule
4 Rule
14 Rule
ECEN 301 Discussion #22 – Combinational Logic 9
Boolean Algebra
Example2: Simplify the equation created by the following truth table
A B C Z0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
ECEN 301 Discussion #22 – Combinational Logic 10
Boolean Algebra
Example2: Simplify the equation created by the following truth table
A B C Z0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
ABCCABCBACBABCACBAZ
ECEN 301 Discussion #22 – Combinational Logic 11
Boolean Algebra
Example2: Simplify the equation created by the following truth table
A B C Z0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
CAZ
ACAZ
BBACAZ
ABBACAZ
CCABCCBABBCAZ
ABCCABCBACBABCACBAZ
ECEN 301 Discussion #22 – Combinational Logic 12
Boolean Algebra
Example3: Determine the truth tableA B C Z0 0 0 ?
0 0 1 ?
0 1 0 ?
0 1 1 ?
1 0 0 ?
1 0 1 ?
1 1 0 ?
1 1 1 ?
A
B
C
Z
ECEN 301 Discussion #22 – Combinational Logic 13
Boolean Algebra
Example3: Determine the truth tableA B C x1 Z
0 0 0 0 ?
0 0 1 0 ?
0 1 0 1 ?
0 1 1 1 ?
1 0 0 1 ?
1 0 1 1 ?
1 1 0 1 ?
1 1 1 1 ?
A
B
C
Z
BAx 1
ECEN 301 Discussion #22 – Combinational Logic 14
Boolean Algebra
Example3: Determine the truth tableA B C x1 x2 Z
0 0 0 0 1 ?
0 0 1 0 1 ?
0 1 0 1 1 ?
0 1 1 1 0 ?
1 0 0 1 1 ?
1 0 1 1 1 ?
1 1 0 1 1 ?
1 1 1 1 0 ?
A
B
C
Z
BAx 1
BCx 2
ECEN 301 Discussion #22 – Combinational Logic 15
Boolean Algebra
Example3: Determine the truth tableA B C x1 x2 x3 Z
0 0 0 0 1 0 ?
0 0 1 0 1 1 ?
0 1 0 1 1 0 ?
0 1 1 1 0 1 ?
1 0 0 1 1 1 ?
1 0 1 1 1 1 ?
1 1 0 1 1 1 ?
1 1 1 1 0 1 ?
A
B
C
Z
BAx 1
BCx 2CAx 3
ECEN 301 Discussion #22 – Combinational Logic 16
Boolean Algebra
Example3: Determine the truth tableA B C x1 x2 x3 Z
0 0 0 0 1 0 0
0 0 1 0 1 1 0
0 1 0 1 1 0 0
0 1 1 1 0 1 0
1 0 0 1 1 1 1
1 0 1 1 1 1 1
1 1 0 1 1 1 1
1 1 1 1 0 1 0
A
B
C
Z
BAx 1
BCx 2CAx 3 CABCBAZ
ECEN 301 Discussion #22 – Combinational Logic 17
Boolean Algebra
Example3: Determine the truth tableA B C x1 x2 x3 Z
0 0 0 0 1 0 0
0 0 1 0 1 1 0
0 1 0 1 1 0 0
0 1 1 1 0 1 0
1 0 0 1 1 1 1
1 0 1 1 1 1 1
1 1 0 1 1 1 1
1 1 1 1 0 1 0
BCA
CBCA
CBACA
CBABBCA
CABCBACBA
CABCBAZ
ECEN 301 Discussion #22 – Combinational Logic 18
Combinational Logic
Decoders
Multiplexers
ECEN 301 Discussion #22 – Combinational Logic 19
Decoders Decode the input and signify its value by raising just one of its
outputs. A decoder with n inputs has 2n outputs
X
Y
Z
W
2-to-4Decoder
A B
W
X
Y
Z
DECODERSymbol
ECEN 301 Discussion #22 – Combinational Logic 20
Decoders Write the truth table
X
Y
Z
W
ECEN 301 Discussion #22 – Combinational Logic 21
Decoders Write the truth table
X
Y
Z
W
A B W X Y Z0 0 1 0 0 0
0 1 0 1 0 0
1 0 0 0 1 0
1 1 0 0 0 1
ECEN 301 Discussion #22 – Combinational Logic 22
Multiplexors Connect one of its inputs to its output according to
select signals
Useful for selecting one from a collection of data inputs.
Usually has 2n inputs and n select lines.
A B
S
C
1 0
MULTIPLEXOR Symbol
ECEN 301 Discussion #22 – Combinational Logic 23
Multiplexors Write the truth table
A B
S
C
1 0
MULTIPLEXOR Symbol
A B S C0 0 0 ?
0 0 1 ?
0 1 0 ?
0 1 1 ?
1 0 0 ?
1 0 1 ?
1 1 0 ?
1 1 1 ?
ECEN 301 Discussion #22 – Combinational Logic 24
Multiplexors Write the truth table
A B
S
C
1 0
MULTIPLEXOR Symbol
A B S C0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
