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7/24/2019 Kanaugh MGA
1/16
Mapa de Karnaugh para duas variveis
A
A
B B
A
A
B B
A
A
B B
A
A
B B
A
A
B B
regio A regio A
regio B regio B
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
2/16
Mapa de Karnaugh para duas variveis
A
A
B B
A
A
B B
A
B B
A
B B
regiao A B regiao A B
AA
regiao A B regiao A B
caso/posio
2
0
!
A
A
B B
regio posio
A B 0
A B A B 2
A B !
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
3/16
Mapa de Karnaugh para duas variveis: e".
2
0 1
3
A
A
B B
pos A B #
0 0 0 0 0
2 0 0
!
00
A
A
B B
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
4/16
Mapa de Karnaugh para duas variveis: e".
pos A B #
0 0 0 0 0
2 0 0
!
0
0
A
A
B B
# $ AB %AB
# $ B
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
5/16
A
A
B B
& & &
A
A
B B
& & &
A
A
B B
& & &
A
A
B B
& & &
A
A
B B
& & &
A
A
B B
& & &
Mapa de
Karnaugh para
'r(s )ariveis
A
A
B B
& & &
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
6/16
Mapa de Karnaugh para 'r(s )ariveis
*
0
+
A
A
B B
,
! 2
-
& & &
regio posio
A B & 0
A B & A B & 2
A B & !
A B & *
A B & +
A B & -
A B & ,
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
7/16
Mapa de Karnaugh para 'r(s )ariveis: e".:
4
0 1
5
A
A
B B
7
3 2
6
C C C
pos. A B & #
0 0 0 0
0 0
2 0 0 ! 0 0
* 0 0 0
+ 0 0
- 0 0
, 0
0
A
A
B B
0
0
& & &
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
8/16
Mapa de Karnaugh para 'r(s )ariveis: e".:
pos. A B & #
0 0 0 0
0 0
2 0 0 ! 0 0
* 0 0 0
+ 0 0
- 0 0
,
0
0
A
A
B B
0
0
& & &
# $ /A /B /& % /A /B & % /A B /& % A B &
# $ /A /B % /A /& % A B &
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
9/16
*
0
+ ,
! 2
-
2 !
+ *
0
A
A
B
B
B
& &
Mapa de Karnaugh para 1ua'ro )ariveis
regio posio
A B & 0
A B &
A B & 2
A B & !
A B & *
A B & +
A B & -A B & ,
A B &
A B &
A B & 0A B &
A B & 2
A B & !
A B & *
A B & +Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
10/16
4
0 1
5 7
3 2
6
8
12 13
9 11
15 14
10
A
A
B
B
B
C C
D DD
Karnaugh para 1ua'ro )ariveis: e".:
pos. A B & #
0 0 0 0 0 0
0 0 0
2 0 0 0 0
! 0 0
* 0 0 0 0
+ 0 0
- 0 0 0, 0
0 0 0 0
0 0 0
0 0 0 0 0
2 0 0 0
! 0 0
* 0
+ 0
00
0
0
0
0 0
0 0
0
A
A
B
B
B
& &
7/24/2019 Kanaugh MGA
11/16
Karnaugh para 1ua'ro )ariveis: e".:
pos. A B & #
0 0 0 0 0 0
0 0 0
2 0 0 0 0
! 0 0
* 0 0 0 0
+ 0 0
- 0 0 0, 0
0 0 0 0
0 0 0
0 0 0 0 0
2 0 0 0
! 0
* 0 0
+ 0
0
0
0
0
0
0 0
0 0
0
A
A
B
B
B
& &
# $ /A /B /& % /A /B & % /A B /&
% /A B & % A /B & % A B /&
# $ /A % A & /
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
12/16
40 1
5 73 2
6
8
12 13
9 11
15 14
10
A
A
B
B
B
C C
D DD
Karnaugh para 1ua'ro )ariveis: e".: 2
pos. A B & #
0 0 0 0 0
0 0 0 0
2 0 0 0
! 0 0 0
* 0 0 0 0
+ 0 0
- 0 0 , 0 0
0 0 0
0 0 0
0 0 0 0 0
2 0 0 0
! 0
* 0 0
+ 0
0
0
0
0
0
0
0 0
0
A
A
B
B
B
& &
7/24/2019 Kanaugh MGA
13/16
Karnaugh para 1ua'ro )ariveis: e".: 2
pos. A B & #
0 0 0 0 0
0 0 0 02 0 0 0
! 0 0 0
* 0 0 0 0
+ 0 0
- 0 0
, 0 0
0 0 0
0 0 0
0 0 0 0 0
2 0 0 0
! 0
* 0 0+ 0
0 0
00
0
0
0 0
0
A
A
B
B
B
& &
# $ /A /B /& / % /A /B & / %
/A B /& % /A B & / %
A /B /& / % A /B & % A B /&
# $ B /& % /A & / %
/B /& / % A /B &
7/24/2019 Kanaugh MGA
14/16
&ondies 3rrelevan'es
uran'e a 4ase de cons'ruo da 5a6ela )erdade7 re4eren'e a
um pro8e'o7 pode9se cons'a'ar even'uais 4al'as de especi4icao
em relao ao nvel l;gico 1ue uma sada deva assumir aoocorrer de'erminada com6inao da de modo
a se o6'er a melhor e"presso
6ooleana possvel.
4a?endo " $ >0>:# $ A
4a?endo " $ >>:
# $ A % /B
7/24/2019 Kanaugh MGA
15/16
&ondies 3rrelevan'es: e".:
pos. A B & #
0 0 0 0 0 0
0 0 0 0
2 0 0 0
! 0 0
* 0 0 0
+ 0 0
- 0 0 , 0 0
0 0 0
0 0
0 0 0 " 0 "
2 0 0 "
! 0 "
* 0 "
+ "
0 0
0
" "
"" "
"
A
A
B
B
B
& &
# $ A % /B & % B /& % & /
Manoel Gomes de Andrade : [email protected]
7/24/2019 Kanaugh MGA
16/16
&asos 1ue no admi'em
simpli4icao 0
0
A
A
B B
0
0
A
A
B B
0
0
A
A
B B
0
0
& & &
0
0
A
A
B B
0
0
& & &
0
0
0
0
0
0
0
0
A
A
B
B
B
& &
0
0
0
0
0
0
0
0
A
A
B
B
B
& &