CIRCUITOS DIGITAIS -ÁLEGEBRA BOOLEANA

Universidade Federal do Maranhão
Disciplina :Circuitos Digitais (2011.2)

Terceira lista de Exercícios (2011.2)
1-Simplifique as expressões boolenas utilizando a álgebra de Boole.

a. S = ABC’ + A’B’C + ABC + A’BC + A’BC ‘ S = ABC’+A’B’C+ABC+A’B(C+C’) S = ABC’+A’B’C+ABC+A’B S = AB(C+C’)+A’B’C+A’B S = AB+A’B’C+A’B S= AB+A’C+A’C+A’ S=A’C+B
b. S = AC + BC + ABC S = A(C+B’C)+B’C S = AB+B’C c. S = ABCD + ABCD + ABCD + ABCD +ABCD + ABCD + ABCD S = D(ABC’+ABC’)+D’(A’B’C+ABC’+A’BC+AB’C) S = ABD+D’C+ABD’ S = AB+D’C

d. S = [ (B + C + D) (A + B + C) + C]+ ABC + B (A + C) S = [(BCD)(AB’C’)+C]+A’B’C+B’(A’C’) S = [(B’+C’+D’)+C(A’+B+C)]+A’B’C+A’B’C’ S = [C(B’+C’+D’+A’+B+C)]+A’B’ S = (B’+CD’+A’C+BC+C+A’B’) S = S=A’B’+C’ e. S = A [ B (C + D) + A (B + C)] + CD + ABC + AB S = A[B’(C’D’)+A’(B’C’)]+CD’+A(B’C+B) S = A[(B+C+D)(A+B+C)]+CD’+A(B+C) S = A[AB+BB+BC+CA+CB+CC+DA+DB+DC]+CD’+A(B+C) S = AB’A+ABC+ACA+ACB+ADA+ADB+ADC+CD’+AB+AC S = AB’+ABC+AC+ACB+AD+ADB+ADC+CD’+AB+AC S = AB+AC(B+1)+A(BC+B)+AC+ADC+CD’ S = AB+AC(B+1)+AD(B+1)+AC(BC+B)+C(A+AD)+CD’ S = AB+AD+CD’

f. S = AB’C’+ AB’C + ABC S = AB’C+AC S = A(B’C+C) S = AC+AB’

g. S=A’C(A’BD)’+A’BC’D+AB’C S = A’C(A+B’+D’)+A’BC’D’+AB’C S = A’B’C+A’CD’+A’BC’D’+AB’C S = B’C+A’CD’+A’BC’D’

h. S= ABC+A’C S = BC+A’C

i. S=(A+B)(B’+A’) S = AB’+AA’+BB’+BA’ S = AB’+BA’

j. S=ABC+AB’C+A’ S = AC(B+B’)+A’ S = A’+C

k. S=(C+D)’+A’CD’+AB’C’+A’B’CD+ACD’ S=C’D’+CD’+AB’C+A’BC+AC S=D’+AB’C+A’BC

l. S=BD+B(D+E)+D(D+F) S = BD+BD+BE+D’D+D’F S = BD+BE+D’F

m. S= A’B’C+(A+B+C’)’+A’B’C’D S = A’’B’C+A’B’C’+A’B’C’D S = AB’C+A’B’C’D(C+D) S = A’B’(C+C’D) S = A’B’C+A’B’D

2-Determine o circuito de cada expressão booleana da questão 1 e o circuito da expressão simplificada