multiple output sop minimization
DESCRIPTION
Multiple Output SOP Minimization. Multiple-Output Minimization. Frequently, practical logic design problems require minimization of multiple-output functions all of which are functions of the same input variables. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/1.jpg)
Multiple Output Multiple Output SOP MinimizationSOP Minimization
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Multiple-Output Minimization• Frequently, practical logic design problems require minimization
of multiple-output functions all of which are functions of the same input variables.
• This is such a tedious task that we relegate it to a computer program, eg, Espresso in the SIS package we see later in the course.
• Here, we will show what needs to be considered in multiple-output minimization, but advise that all such work be performed with the aid of a computer, ie, use a CAD tool.
![Page 3: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/3.jpg)
Example of Multiple-output Minimization
• To illustrate multiple-output minimization, consider the following three output expressions, each of three variables:
f A B C m
f A B C m
f A B C m
1
2
3
0 3 4 5 6
1 2 4 6 7
13 4 5 6
( , , ) ( , , , , )
( , , ) ( , , , , )
( , , ) ( , , , , )
![Page 4: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/4.jpg)
Minimizing f1
f1 = B’C’ + AB’ + AC’ + A’BC
1 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11 1
![Page 5: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/5.jpg)
Minimizing f2
f2 = A’B’C + BC’ + AB + AC’
0 0
BC
A 00 01
1
0 1
54
13 2
67
11 10
A
B
C
1
0 1 11
![Page 6: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/6.jpg)
Minimizing f3
f3 = A’C + AB’ + B’C + AC’
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
1 0 11
![Page 7: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/7.jpg)
Shared Shared Prime Prime
ImplicantsImplicants
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Using Shared PIsUsing Shared PIs
• The object is to minimize each of the three functions in such a way as to retain as many shared terms between them as possible, thus optimizing the combinational logic of this system.
• Hence, we now need to look at the shared terms.
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AND-ed functions: f1.f2
f1 . f2 = AC’
0 0
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
0 0 11
)6,4(. 21 mff
![Page 10: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/10.jpg)
AND-ed functions: f2.f3
f2 . f3 = AC’ + A’B’C
0 0
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
0 0 11
f f m2 3 1 4 6. ( , , )
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AND-ed functions: f3.f1
f3 . f1 = AC’ + AB’ + A’BC
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11
f f m3 1 3 4 5 6. ( , , , )
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AND-ed functions: f1.f2 .f3
f1 . f2 . f3 = AC’
0 0
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
0 0 11
f f f m1 2 3 4 6. . ( , )
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Summarizing Product Terms The original functions are:
f1 = B’C’ + AB’ + AC’ + A’BC f2 = A’B’C + BC’ + AB + AC’ f3 = A’C + AB’ + B’C + AC’
The product terms, which must be included in the optimized expressions, are: f1 . f2 . f3 = AC’ - common to all three. f1 . f2 = AC’ f2 . f3 = AC’ + A’B’C f3 . f1 = AC’ + AB’ + A’BC
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Including Shared PI: AC’
1 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11
0 0
BC
A 00 01
1
0 1
54
13 2
67
11 10
A
B
C
1
0 1 11
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
1 0 11
f1 = AC’
f2 = AC’
f3 = AC’
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Including Shared PI: A’B’C
1 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11
0 0
BC
A 00 01
1
0 1
54
13 2
67
11 10
A
B
C
1
0 1 11
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
1 0 11
f1 = AC’
f2 = AC’ + A’B’C
f3 = AC’ + A’B’C
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Including Shared PI: AB’
1 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11
0 0
BC
A 00 01
1
0 1
54
13 2
67
11 10
A
B
C
1
0 1 11
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
1 0 11
f1 = AC’ + AB’
f2 = AC’ + A’B’C
f3 = AC’ + A’B’C + AB’
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Including Shared PI: A’BC
1 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11
0 0
BC
A 00 01
1
0 1
54
13 2
67
11 10
A
B
C
1
0 1 11
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
1 0 11
f1 = AC’ + AB’ + A’BC
f2 = AC’ + A’B’C
f3 = AC’ + A’B’C + AB’ + A’BC
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Including Remaining PIs
1 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
0
1 0 11
0 0
BC
A 00 01
1
0 1
54
13 2
67
11 10
A
B
C
1
0 1 11
0 1
BC
A 00 01
1
0 1
54
03 2
67
11 10
A
B
C
1
1 0 11
f1 = AC’ + AB’ + A’BC + B’C’
f2 = AC’ + A’B’C + AB + BC’
f3 = AC’ + A’B’C + AB’ + A’BC
![Page 19: Multiple Output SOP Minimization](https://reader036.vdocuments.mx/reader036/viewer/2022062814/56816834550346895ddde958/html5/thumbnails/19.jpg)
What have we learnt?• Multiple-output minimization is not for the faint hearted.• You should be able to find reasonably good solutions
from 5-variable Kmaps.• Good understanding of these principles will help you to
understand how software for SOP minimization works, coming very soon
• For any practical problem, use a suitable CAD package.• The principles illustrated above are used to create
efficient programs for multiple-output minimization.