Ejercicios de Funciones Lógicas

1998. Septiembre, original (sistemas).
✎ Encuentre las expresiones canónicas de la función f (A, B, C, D) = A ⋅ B + C .
Solución:
Desdoblando en minterms:
A ⋅ B = A ⋅ B ⋅ C + A ⋅ B ⋅ C = A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D
C = A ⋅ C + A ⋅ C
A ⋅ C = A ⋅ B ⋅ C + A ⋅ B ⋅ C = A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D
A ⋅ C = A ⋅ B ⋅ C + A ⋅ B ⋅ C = A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D
Eliminando términos repetidos:
f = A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D +
A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D + A ⋅ B ⋅ C ⋅ D
f = m2 + m3 + m6 + m7 + m8 + m9 + m10 + m11 + m14+ m15
Para pasar a la expresión en maxterms, llevamos acabo estos dos pasos:
1.- Encontrar los minterms ausentes: m0 + m1 + m4 + m5 + m12 + m13
2.- Complementar a 15 los subíndices: 15 14 11 10 3 2
f = M2 ⋅ M3 ⋅ M10 ⋅ M11 ⋅ M14 ⋅ M15
1999. Febrero. Segunda semana.
✎ Encuentre cuál de las cuatro funciones lógicas de tres variables f(A, B, C) dadas a continuación representa una función
lógica diferente de las otras tres.
a) m 1 + m 3 + m 4
b) (A + C)
⋅ ( A + B + C)
c) A ⋅ (B + C) + A ⋅ C
d) A ⋅ C + B ⋅ C
Solución:
Las transformaremos a suma de productos, para poder compararlas:
a) m1 + m3 + m4
b) 4 m
(A + C)
⋅ ( A + B + C) = A + C + A + B + C = A ⋅ C + A ⋅B
⋅ C = A ⋅B
⋅ C + A ⋅B
⋅ C + A ⋅B
⋅ C = m1
+ m3
+
b)
A ⋅ (B + C) + A ⋅ C = A ⋅ (B + C) ⋅ A ⋅ C = ( A + ( B + C))
⋅ (A + C) = ( A + B ⋅ C)
⋅ (A + C) = A ⋅ A + A ⋅ C + A ⋅ B ⋅ C + C ⋅ B ⋅ C
A ⋅ C + A ⋅ B ⋅ C =
A ⋅ B ⋅ C + A ⋅ B ⋅ C + A ⋅ B ⋅ C = m1
+ m3
+ m4
c) 4 m
A ⋅ C + B ⋅ C = A ⋅B
⋅ C + A ⋅B
⋅ C + A ⋅B
⋅ C + A ⋅B
⋅ C = m0
+ m1
+ m3
+ Esta es la diferente.
Ejercicios de Funciones Lógicas 8