11. m S P E CS CP CE
0 0 0 0 0 0 0
1 0 0 1 0 0 1
2 0 1 0 0 1 0
3 0 1 1 0 1 0
4 1 0 0 1 0 0
5 1 0 1 1 0 0
6 1 1 0 1 0 0
7 1 1 1 1 0 0
CS (S, P, E ) = S P’ E’ + S P’ E
12. m S P E CS CP CE
0 0 0 0 0 0 0
1 0 0 1 0 0 1
2 0 1 0 0 1 0
3 0 1 1 0 1 0
4 1 0 0 1 0 0
5 1 0 1 1 0 0
6 1 1 0 1 0 0
7 1 1 1 1 0 0
CS (S, P, E ) = S P’ E’ + S P’ E + S P E’
13. m S P E CS CP CE
0 0 0 0 0 0 0
1 0 0 1 0 0 1
2 0 1 0 0 1 0
3 0 1 1 0 1 0
4 1 0 0 1 0 0
5 1 0 1 1 0 0
6 1 1 0 1 0 0
7 1 1 1 1 0 0
CS (S, P, E ) = S P’ E’ + S P’ E + S P E’ + S P E
14. CS (S, P, E ) = S P’ E’ + S P’ E + S P E’ + S P E
CS (S, P, E ) = S P’ (E’+E)+ S P (E’+E)
CS (S, P, E ) = S P’ + S P
CS (S, P, E ) = S (P’+P)
CS (S, P, E ) = S
15. m S P E CS CP CE
0 0 0 0 0 0 0
1 0 0 1 0 0 1
2 0 1 0 0 1 0
3 0 1 1 0 1 0
4 1 0 0 1 0 0
5 1 0 1 1 0 0
6 1 1 0 1 0 0
7 1 1 1 1 0 0
CS (S, P, E ) = S P’ E’ + S P’ E + S P E’ + S P E
CS (S,) = S
16. m S P E CS CP CE
0 0 0 0 0 0 0
1 0 0 1 0 0 1
2 0 1 0 0 1 0
3 0 1 1 0 1 0
4 1 0 0 1 0 0
5 1 0 1 1 0 0
6 1 1 0 1 0 0
7 1 1 1 1 0 0
CS (S, P, E ) = S P’ E’ + S P’ E + S P E’ + S P E = S
CS (S,) = S
17. m S P E CS CP CE
0 0 0 0 0 0 0
1 0 0 1 0 0 1
2 0 1 0 0 1 0
3 0 1 1 0 1 0
4 1 0 0 1 0 0
5 1 0 1 1 0 0
6 1 1 0 1 0 0
7 1 1 1 1 0 0
CP (S, P, E ) = S’ P E’ + S’ P E
CP (S, P, E ) = S’ P (E’+E)
CP (S, P, E ) = S’ P
CP (S, P ) = S’ P
19. m A B C X
0 0 0 0 1
1 0 0 1 1
2 0 1 0 1
3 0 1 1 0
4 1 0 0 0
5 1 0 1 0
6 1 1 0 0
7 1 1 1 0
FX (A,B,C) = A’ B’ C’ + A’ B’ C + A’ B C’
FX (A,B,C) = A’ B’ C’ + A’ B’ C
+ A’ B C’ + A’ B’ C’
FX (A,B,C) = A’ B’ + A’ C’
FX (A,B,C) = A’ (B’ + C’)
28. F= A’ B + A B’ + A B + A’ C’
F= B + A + A’ C’
F= B + (A+ A’)(A+ C’)
F= B + A+ C’ F= A+B+C’
29. Actividad
Usando como recursos
• Factorización
• Duplicando un termino ya existente
• Teorema del consenso
• Propiedad distributiva
• Identidades
• Teorema de Dmorgan
Resuelva las siguientes funciones
30. 1.-Identidades
2.- Factorización
AB’ + AB = A(B’+B)= A
3.- Propiedad Distributiva
X+YZ = (X+Y) (X+Z)
X (Y+Z) = XY +XZ
4.-Teorema del consenso
AB+A’C+BC = AB+A’C
5.-Teorema de Dmorgan
(AB)’=A’+ B’ (A+B)’=A’ B’
A+B =(A’ B’)’ AB =(A’+B’)’
AND OR
A A=A A + A=A
A 0 =0 A + 0 = A
A 1 =A A + 1 =1
A A’ =0 A+A’ =1 1
1+ B’+ C
2
DC’(0)
3
A’+B+A
4
A+ A’ BC
5
A’BC+A’BC’
31. F1 (B,C)= 1+B’+C
F1 (B,C)= 1
1.-Identidades
2.- Factorización
AB’ + AB = A(B’+B)= A
3.- Propiedad Distributiva
X+YZ = (X+Y) (X+Z)
X (Y+Z) = XY +XZ
4.-Teorema del consenso
AB+A’C+BC = AB+A’C
5.-Teorema de Dmorgan
(AB)’=A’+ B’ (A+B)’=A’ B’
A+B =(A’ B’)’ AB =(A’+B’)’
AND OR
A A=A A + A=A
A 0 =0 A + 0 = A
A 1 =A A + 1 =1
A A’ =0 A+A’ =1
32. F2 (D,C)= DC’(0)
F2 (D,C)= 0
1.-Identidades
2.- Factorización
AB’ + AB = A(B’+B)= A
3.- Propiedad Distributiva
X+YZ = (X+Y) (X+Z)
X (Y+Z) = XY +XZ
4.-Teorema del consenso
AB+A’C+BC = AB+A’C
5.-Teorema de Dmorgan
(AB)’=A’+ B’ (A+B)’=A’ B’
A+B =(A’ B’)’ AB =(A’+B’)’
AND OR
A A=A A + A=A
A 0 =0 A + 0 = A
A 1 =A A + 1 =1
A A’ =0 A+A’ =1
33. F3 (A, B) = A’+B+A
F3 (A, B) = 1
1.-Identidades
2.- Factorización
AB’ + AB = A(B’+B)= A
3.- Propiedad Distributiva
X+YZ = (X+Y) (X+Z)
X (Y+Z) = XY +XZ
4.-Teorema del consenso
AB+A’C+BC = AB+A’C
5.-Teorema de Dmorgan
(AB)’=A’+ B’ (A+B)’=A’ B’
A+B =(A’ B’)’ AB =(A’+B’)’
AND OR
A A=A A + A=A
A 0 =0 A + 0 = A
A 1 =A A + 1 =1
A A’ =0 A+A’ =1
34. F4 (A,,B,C) = A+A’BC
F4 (A,,B,C)=(A+A’)(A+BC)
F4 (A,,B,C)=A+BC
1.-Identidades
2.- Factorización
AB’ + AB = A(B’+B)= A
3.- Propiedad Distributiva
X+YZ = (X+Y) (X+Z)
X (Y+Z) = XY +XZ
4.-Teorema del consenso
AB+A’C+BC = AB+A’C
5.-Teorema de Dmorgan
(AB)’=A’+ B’ (A+B)’=A’ B’
A+B =(A’ B’)’ AB =(A’+B’)’
AND OR
A A=A A + A=A
A 0 =0 A + 0 = A
A 1 =A A + 1 =1
A A’ =0 A+A’ =1