EDI18701 AULA07

Teoremas Booleanos

(1) $A.0=0\,$

(2) $A.1=A\,$

(3) $A.A=A\,$

(4) $A.{\bar {A}}=0\,$

(5) $A+0=A\,$

(6) $A+1=1\,$

(7) $A+A=A\,$

(8) $A+{\bar {A}}=1\,$

(9) $A+B=B+A\,$

(10) $A.B=B.A\,$

(11) $A+(B+C)=(A+B)+C=A+B+C\,$

(12) $A(B.C)=(A.B).C=A.B.C\,$

(13a) $A(B+C)=AB+AC\,$

(13b) $(A+B).(C+D)=AC+AD+BC+BD\,$

(14) $A+(AB)=A\,$

(15a) $A+({\bar {A}}B)=A+B\,$

(15b) ${\bar {A}}+(AB)={\bar {A}}+B\,$

Exemplos

(a) $A{\bar {B}}C+{\bar {A}}{\bar {B}}{\bar {C}}=...\,$

(b) $A{\bar {B}}D+A{\bar {B}}{\bar {D}}=...\,$

(c) $({\bar {A}}+B).(A+B)=...\,$

(d) $ACD+{\bar {A}}BCD=...\,$

(e) $S=A{\bar {C}}+AB{\bar {C}}=...\,$

(f) $S={\bar {A}}{\bar {B}}C{\bar {D}}+{\bar {A}}{\bar {B}}{\bar {C}}{\bar {D}}=...\,$

(g) $S={\bar {A}}D+ABD=...\,$

Exercícios Propostos

$S_{1}=(A+B+C).({\bar {A}}+B+{\bar {C}})$

$S_{2}=({\overline {{\overline {AC}}+B+D}})+C({\overline {ACD}})$

$S_{3}=({\overline {(A+B).C}})+({\overline {D(C+B)}})$

$S_{4}=({\bar {A}}+{\bar {B}}+{\bar {C}}).(A+B+{\bar {C}})$

$S_{5}={\bar {A}}.{\bar {B}}.C+{\bar {A}}.B.C+{\bar {A}}.B.{\bar {C}}+A.B.C+A.B{\bar {C}}$

Material de Apoio

• [Slides da Aula]

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