Lista_Exercicios_n3.Gab

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1 
Disciplina: Eletrônica Digital 
Professora: Priscila Doria 
Nome do aluno: 
 
Lista de Exercícios Nº 3 
 
1. Simplifique as expressões abaixo, utilizando a Álgebra de Boole. 
 
a. CBABCAABCCBACABS ++++= 
 
Resposta: BCAS += 
 
b. ABCDDCBADABCDBCADCABDCBADCABS ++++++= 
 
Resposta: DCABS += 
 
c. )(]))([( CABCBACCBADCBS ++++++++= 
 
Resposta: BACS += 
 
d. ABCBADCCBADCBAS ++++++= ])()([ 
 
Resposta: ACADABDCS +++= 
 
e. DABADCBDDCBBAS +++++⊕= ])()[( 
 
Resposta: ABDCBADAS ++= 
 
f. )]()())(([ BAACBCACBCBAACDDCBS +++++++++= 
 
Resposta: ACBS += 
 
g. }])([){( ACBACBADCBADDCBAS ++++⊕++= 
 
Resposta: DCAS = 
 
h. }])()[(){( ABDDBCBDABCBACBBBAS +++++⊕++= 
 
Resposta: DBBAS += 
 
i. ABCCBABCACBACBAS ++++= 
 
Resposta: BAACBAS ++= 
 
 
 
 
 2 
 
j. DCBAABCDDCBABCDADCABDCBACDBADCBAS +++++++= 
 
Resposta: CBABCDDCADCBS +++= 
 
k. CACDBADCBAADBS ++++= 
 
Resposta: BAS += 
 
l. DCBADCBCDBDBCDAABABCS ++++++= 
 
Resposta: CBBDACCBS +++= 
 
2. Simplifique a expressão e desenhe o circuito que executa a expressão simplificada. 
 
})]([){( DCBACBCBADCBDBS +++++⊗++= 
 
 
 
3. Demonstre que: 
 
)()( CBACBAS ⊗⊕=⊕⊗= 
 
4. Prove que: 
DCBADCBA ⊗⊗⊗=⊕⊕⊕ 
 
A B C D DCBA ⊕⊕⊕ DCBA ⊗⊗⊗ 
0 0 0 0 1 1 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 0 1 1 1 1 
0 1 0 0 0 0 
0 1 0 1 1 1 
0 1 1 0 1 1 
0 1 1 1 0 0 
1 0 0 0 0 0 
1 0 0 1 1 1 
1 0 1 0 1 1 
1 0 1 1 0 0 
1 1 0 0 1 1 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 1 1 1 1 1 
 
5. Simplifique as expressões da questão 1, utilizando o diagrama de Veitch-Karnaugh. 
 
 
 
 
 3 
 
6. Através dos diagramas de Veitch-Karnaugh, determine a expressão simplificada de S1 e S2. 
 
a. A B S1 S2 
0 0 1 1 
0 1 0 1 
1 0 1 0 
1 1 1 0 
 
 
 
 
 
Respostas: BAS +=1 e AS =2 
b. A B C S1 S2 
0 0 0 X 1 
0 0 1 0 X 
0 1 0 1 0 
0 1 1 X 0 
1 0 0 1 0 
1 0 1 X 1 
1 1 0 X X 
1 1 1 1 X 
 
Respostas: BAS +=1 e ACBAS +=2 
c. A B C D E S1 S2 
0 0 0 0 0 1 1 
0 0 0 0 1 1 0 
0 0 0 1 0 1 1 
0 0 0 1 1 1 0 
0 0 1 0 0 0 1 
0 0 1 0 1 1 1 
0 0 1 1 0 0 1 
0 0 1 1 1 1 1 
0 1 0 0 0 0 1 
0 1 0 0 1 0 0 
0 1 0 1 0 1 1 
0 1 0 1 1 0 0 
0 1 1 0 0 1 1 
0 1 1 0 1 1 1 
0 1 1 1 0 0 1 
0 1 1 1 1 1 1 
1 0 0 0 0 1 1 
1 0 0 0 1 1 0 
1 0 0 1 0 0 1 
1 0 0 1 1 0 1 
1 0 1 0 0 0 1 
1 0 1 0 1 1 1 
1 0 1 1 0 0 1 
1 0 1 1 1 1 1 
1 1 0 0 0 0 1 
1 1 0 0 1 0 0 
1 1 0 1 0 1 1 
1 1 0 1 1 0 0 
1 1 1 0 0 0 1 
1 1 1 0 1 1 1 
1 1 1 1 0 0 1 
1 1 1 1 1 1 1 
 
Respostas: 
DBAECS
EDCBDBCADCBCBACES
++=
++++=
2
1 
d. A B C D E S1 S2 
0 0 0 0 0 0 1 
0 0 0 0 1 0 X 
0 0 0 1 0 1 1 
0 0 0 1 1 0 X 
0 0 1 0 0 1 X 
0 0 1 0 1 1 1 
0 0 1 1 0 0 X 
0 0 1 1 1 1 1 
0 1 0 0 0 0 1 
0 1 0 0 1 1 0 
0 1 0 1 0 1 1 
0 1 0 1 1 0 0 
0 1 1 0 0 1 X 
0 1 1 0 1 1 1 
0 1 1 1 0 0 0 
0 1 1 1 1 1 1 
1 0 0 0 0 0 1 
1 0 0 0 1 0 X 
1 0 0 1 0 1 1 
1 0 0 1 1 0 0 
1 0 1 0 0 1 X 
1 0 1 0 1 1 1 
1 0 1 1 0 0 0 
1 0 1 1 1 1 1 
1 1 0 0 0 0 X 
1 1 0 0 1 0 1 
1 1 0 1 0 1 1 
1 1 0 1 1 0 1 
1 1 1 0 0 1 1 
1 1 1 0 1 1 X 
1 1 1 1 0 0 1 
1 1 1 1 1 1 X 
 
Respostas: 
ECABS
EDCDCCES
⊗+=
++=
2
1 
 
 
 
 
 4 
 
7. Simplifique as expressões de S1, S2, S3, S4, utilizando os mapas de Veitch-Karnaugh. 
 
a. A B C D S1 S2 S3 S4 
0 0 0 0 1 1 0 0 
0 0 0 1 1 0 0 0 
0 0 1 0 1 1 1 0 
0 0 1 1 1 0 0 1 
0 1 0 0 1 1 1 1 
0 1 0 1 0 1 1 1 
0 1 1 0 0 1 1 0 
0 1 1 1 1 1 0 1 
1 0 0 0 1 1 0 0 
1 0 0 1 1 1 0 1 
1 0 1 0 1 0 1 0 
1 0 1 1 1 0 0 0 
1 1 0 0 1 0 0 0 
1 1 0 1 0 1 1 1 
1 1 1 0 0 0 0 1 
1 1 1 1 1 1 0 1 
 
Respostas: 
CDDCBS ++=1 
CBABDDAS ++=2 
DCBDCBDBAS ++=3 
DCAABCCDACBAS +++=4 
b. 
 
Respostas: 
DBS +=1 
DBACBDS ++=2 
CDBAABCCBADBS +++=3 
ABCDADCBS +++=4 
A B C D S1 S2 S3 S4 
0 0 0 0 1 X 0 X 
0 0 0 1 X X 0 0 
0 0 1 0 X 1 0 X 
0 0 1 1 X 0 1 1 
0 1 0 0 1 X X 1 
0 1 0 1 0 1 X X 
0 1 1 0 X 0 1 0 
0 1 1 1 X 1 0 1 
1 0 0 0 X 1 X 0 
1 0 0 1 1 0 1 1 
1 0 1 0 X X 0 0 
1 0 1 1 1 1 0 X 
1 1 0 0 X 0 1 1 
1 1 0 1 X 1 0 1 
1 1 1 0 1 1 X 1 
1 1 1 1 0 X 1 X 
c. A B C S1 S2 S3 S4 
0 0 0 1 1 0 0 
0 0 1 0 1 1 1 
0 1 0 1 1 0 1 
0 1 1 1 0 0 0 
1 0 0 1 1 1 1 
1 0 1 1 1 1 0 
1 1 0 0 1 1 1 
1 1 1 1 0 0 1 
 
Respostas: 
BAACCBS ++=1 
CBS +=2 
CACBS +=3 
CBABCACBAS +++=4