Kanaugh MGA

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  • 7/24/2019 Kanaugh MGA

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    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]

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    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]

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    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]

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    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]

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    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]

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    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]

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    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]

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    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]

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    *

    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]

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    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

    & &

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    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]

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    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

    & &

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    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 &

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    &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

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    &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]

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    &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

    & &