
- •Одесса 2013
- •Вибір варіанту завдання
- •Визначення булевої функції
- •Опис мінімізації булевої функції заданими методами
- •Мінімізація булевої функції методом карт Карно
- •Аналіз синтезованої схеми методом π-алгоритму
- •Гса автомату Мілі
- •Скорочені формули для автомату Мілі
- •Гса автомату Мура
- •Скорочені формули для автомату Мура
Опис мінімізації булевої функції заданими методами
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Ядро AC
(D+E+F+G)*(H+P)*(B+I)*(H+P)*(P+Q)*(D+E+J)*(D+F)*(E+G+L)*(F+G+H+P)*(I+M+Q)*
(B+E+I+J+L)*(F+H+O+P)*(G+L+P+Q)*(M+Q)*(J+N)*(I+L+M+N+Q)*(O+P+Q)*
(M+N+O+Q)=
=
(H+P)*(B+I)*(P+Q)*(D+E+J)*(D+F)*(E+G+L)*(M+Q)*(J+N)=
(H+P)*(P+Q)=HP+HQ+P+PQ=P(H+1+Q)+HQ=P+HQ
(D+E+J)*(D+F)=D+DE+DJ+FD+FE+FJ=D(1+E+J+F)+FE+FJ=D+FE+FJ
(P+HQ)*(D+FE+FJ)*(B+I)*(E+G+L)*(M+Q)*(J+N)=
(P+HQ)*(M+Q)=PM+PQ+HQ
(D+FE+FJ)*(E+G+L)=DE+DG+DL+FE+FJG+FJL
(DE+DG+DL+FE+FJG+FJL)*(J+N)= JDE+JDG+JDL+JFE+FJG+FJL+NDE+NDG+NDL+NFE
(JDE+JDG+JDL+JFE+FJG+FJL+NDE+NDG+NDL+NFE)*(B+I)= BJDE+BJDG+BJDL+BJFE+BFJG+BFJL+BNDE+BNDG+BNDL+BNFE+IJDE+IJDG+IJDL+
IJFE+IFJG+IFJL+INDE+INDG+INDL+INFE
(BJDE+BJDG+BJDL+BJFE+BFJG+BFJL+BNDE+BNDG+BNDL+BNFE+IJDE+IJDG+IJDL+
IJFE+IFJG+IFJL+INDE+INDG+INDL+INFE)*(PM+PQ+HQ)=
PMBJDE+PMBJDG+PMBJDL+PMBJFE+PMBFJG+PMBFJL+PMBNDE+PMBNDG+PMBNDL+PMBNFE+PMIJDE+PMIJDG+PMIJDL+PMIJFE+PMIFJG+PMIFJL+PMINDE+PMINDG+PMINDL+PMINFE+PQBJDE+PQBJDG+PQBJDL+PQBJFE+PQBFJG+PQBFJL+PQBNDE+PQBNDG+PQBNDL+PQBNFE+PQIJDE+PQIJDG+PQIJDL+PQIJFE+PQIFJG+PQIFJL+
PQINDE+PQINDG+PQINDL+PQINFE+HQBJDE+HQBJDG+HQBJDL+HQBJFE+HQBFJG+HQBFJL+HQBNDE+HQBNDG+HQBNDL+HQBNFE+HQIJDE+HQIJDG+HQIJDL+
HQIJFE+HQIFJG+HQIFJL+HQINDE+HQINDG+HQINDL+HQINFE
П1= PMBJDE
ОБ С ЯДРО AC =
=8+26+5=39
П2= PMBJDG
ОБ С ЯДРО AC=
=8+25+4=37
П2= PMBJDL
ОБ С ЯДРО AC=
=8+25+4=37
П2= PMBJFE
ОБ С ЯДРО AC=
=8+25+5=38
МДНФ=Покрытие П2 минимальное
Y=x1~x4+x1x2x4+~x1x2~x3x4+~x1x4x5+~x1~x2x5+~x1~x3x5+x2~x4x5+x2x3~x4~x5
x1x2/3x4x5
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Y = x1~x4 + x2x3~x4~x5 + x2~x3x4 + ~x1~x2x3x4 + ~x1~x2x5 + ~x1~x3x5 + ~x1x4x5
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1011~
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10~1~*
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ЯДРО ABCDEFGH
П1= ЯДРО
ABCDEFGH =
=8+33+5
МДНФ=Покрытие П1минимальное
Y=(x1+~x2+~x3+x4+~x5)*(x1+~x2+~x3+~x4+x5)*(x1+x2+x3+x5)*(x1+x2+x4+x5)*
(x1+x3+x4+x5)*(x2+x3+~x4+x5)*( ~x1+x2+~x4+x5)*( ~x1+x2+~x4)