Métodos de simplificación

TALLER RESOLUCION ALGEBRAICA, GRAFICA Y ALGORITMICA

1. Para la siguiente tabla de verdad:

X | Y | Z | S1 | S2 |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 1 |1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 0 |

Demostrar de manera algebraica que:

S1 = (X.Y)+Z

S1 = (X+Y+Z)(X+Y+Z)( X+Y+Z)Z+[(X+Y)(X+Y)( X+Y)] TEOREMA DISTRIBUTIVIDAD
Z+[X(Y. Y)( X+Y)] TEOREMA DISTRIBUTIVIDAD
Z+[X( X+Y)] TEOREMA COMPLEMENTOS
Z+[(X. X)+(X.Y)] TEOREMA DISTRIBUTIVIDAD
Z+(X.Y) TEOREMA COMPLEMENTOS(X.Y)+Z TEOREMA CONMUTATIVIDAD

S2 = (X.Y).Z

S2 = (XYZ)+( XYZ)+(XYZ)
S2 = X.(YZ+YZ)+(XYZ) TEOREMA DISTRIBUTIVIDAD
S2 = X.(Z)+(XYZ) TEOREMA COMBINACION
S2 = XZ+(XYZ) ELIMINARPARENTESIS
S2 = Z.(X+XY) TEOREMA DISTRIBUTIVIDAD
S2 = Z.(X+Y) TEOREMA ABSORCION
S2 = Z.(X.Y) TEOREMA MORGAN
S2 = (X.Y).Z TEOREMA CONMUTATIVIDAD

2. Mediante el método desimplificación a través de Mapas de Karnaug, diseñe un circuito digital cuya salida sea uno siempre y cuando la representación binaria de sus entradas sean los valores decimales representados por la función∑m(0,4,6,7,8,12,14,15,16,20,21,22,23,30,31).

A | B | C | D | E | DECIMAL |
0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 4 |
0 | 0 | 1 | 1 | 0 | 6 |
0 | 0 | 1 | 1 | 1 | 7 |
0 | 1 | 0 | 0 | 0 | 8 |0 | 1 | 1 | 0 | 0 | 12 |
0 | 1 | 1 | 1 | 0 | 14 |
0 | 1 | 1 | 1 | 1 | 15 |
1 | 0 | 0 | 0 | 0 | 16 |
1 | 0 | 1 | 0 | 0 | 20 |
1 | 0 | 1 | 0 | 1 | 21 |
1 | 0 | 1 | 1 | 0 | 22 |
1 | 0 |1 | 1 | 1 | 23 |
1 | 1 | 1 | 1 | 0 | 30 |
1 | 1 | 1 | 1 | 1 | 31 |

CDE | CDE | CDE | CDE | CDE | CDE | CDE | CDE | CDE |
AB | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100 |
AB | 1
| || | 1
| 1
| | 1
|
OO | | | | | | | | |
AB | 1
| | | | 1
| 1
| | 1
|
O1 | | | | | | | | |
AB | | | | | 1
1
1
1
| | | |
11 | | | | |...