Задание 1.2
ƒ(
,
,
)=1
|
xyz |
|
|
|
|
|
|
000 |
0 |
1 |
1 |
1 |
1 |
|
001 |
0 |
1 |
1 |
0 |
0 |
|
010 |
0 |
1 |
0 |
0 |
0 |
|
011 |
0 |
1 |
0 |
1 |
1 |
|
100 |
0 |
0 |
0 |
0 |
0 |
|
101 |
1 |
0 |
0 |
1 |
0 |
|
110 |
0 |
0 |
1 |
1 |
1 |
|
111 |
1 |
0 |
1 |
0 |
1 |
=
=1⊕
=
⊕
=
⊕
=
⊕
=
{(000),(011),(110),(111)}
СДНФ(ƒ)
= (x
)v(
y z)v(x
y
)v(x
y z) r(СДНФ(ƒ))
= 12
Геометрический метод
Я
=
=yz
Я
=
xy
Я
=
=
ДНФсокр.(ƒ) = yzvxyv
r(ДНФсокр.(ƒ)) = 7
ДНФядр.(ƒ) = yzvxyv
ДНФсокр. (ƒ) = ДНФядр.
(ƒ) = ДНФтуп. (ƒ) = ДНФmin(ƒ) =yzvxyv
r(ДНФтуп.(ƒ)) =r(ДНФmin(ƒ)) = 7
Метод Квайна
|
|
000* |
|
|
|
|
|
|
|
011 110 |
-11* 11-* |
|
|
111 |
|
|
Дс.
|
000* |
011* |
110* |
111 |
|
Я 000 |
⊕ |
|
|
|
|
Я -11 |
|
⊕ |
|
+ |
|
Я 11- |
|
|
⊕ |
+ |
ДНФсокр. (ƒ) = ДНФядр.
(ƒ) = ДНФтуп. (ƒ) = ДНФmin(ƒ) =yzvxyv
r(ДНФтуп.(ƒ)) =r(ДНФmin(ƒ)) = 7
Задание 1.3
ƒ(
,
,
,
)
= (0100 1011 1010 1010)
=
{(0001),(0100),(0110),(0111),(1000),(1010),(1100),(1110)}
r(СДНФ(ƒ)) = 32
СДНФ(ƒ) =
v
v
v
v
v
v
v
=
v
v
v
v
v
v
v
v
=
=
=
=
=
=
=
=
Метод Карно
|
|
00 |
01 |
11 |
10 |
|
00 |
|
1* |
|
|
|
01 |
1* |
|
1* |
1 |
|
11 |
1 |
|
|
1 |
|
10 |
1* |
|
|
1* |
Я
=
→Я
=
Я
=
→Я
=
Я
=
→Я
=
Я
=
→Я
=
ДНФсокр. (ƒ) =
v
v
v
=
v
v
v
ДНФядр. (ƒ) =
v
v
v
=
ƒ = ДНФтуп. (ƒ) = ДНФmin(ƒ) =
v
v
v
v
r(ДНФсокр.
(ƒ)) =r(ДНФядр.(ƒ))
r(ДНФтуп.(ƒ))
=r(ДНФmin(ƒ))
= 11
Метод Квайна
|
|
|
|
|
|
|
0001* 0100 1000 |
01-0 -100 10-0 1-00 |
-1-0* -1-0 1--0* 1--0 |
|
|
0110 1010 1100 |
011-* -110 1-10 11-0 |
|
|
|
0111 1110 |
|
|
v
v
v
=
v
v
v
v
r(ДНФсокр.(ƒ)) = 11
|
Дс.
|
0001* |
0100* |
0110 |
0111* |
1000* |
1010* |
1100 |
1110 |
|
Я -1-0 |
|
⊕ |
+ |
|
|
|
+ |
+ |
|
Я 1--0 |
|
|
|
|
⊕ |
⊕ |
+ |
+ |
|
Я 011- |
|
|
+ |
⊕ |
|
|
|
|
|
Я 0001 |
⊕ |
|
|
|
|
|
|
|
ДНФядр.(ƒ) =
v
v
v
=
ƒ = ДНФтуп.(ƒ) = ДНФmin(ƒ) =
v
v
v
v
r(ДНФядр.(ƒ)) =r(ДНФтуп.(ƒ)) =r(ДНФmin(ƒ)) = 11
Задание 1.4
ƒ(
,
,
,
)
= (0001 1101 0011 1110)
=
{(0011),(0100),(0101),(0111),(1010),(1011),(1100),(1101),(1110)}
r(СДНФ(ƒ)) = 36
СДНФ(ƒ) =
v
v
v
v
v
v
v
v
v
Метод Карно
|
|
00 |
01 |
11 |
10 |
|
00 |
|
|
1 |
|
|
01 |
1* |
1 |
1 |
|
|
11 |
1 |
1* |
|
1 |
|
10 |
|
|
1 |
1 |
Я
=
→Я
=
=
→
=
=
→
=
=
→
=
=
→
=
=
→
=
=
→
=
ДНФсокр. (ƒ) =
v
v
v
v
v
v
r(ДНФсокр. (ƒ)) = 20
ДНФядр.(ƒ) =
≠ ƒ
P = (
v
)
(
v
)(
v
)(
v
)
(
v
)(
v
)(
v
)
=
=
(
v
v
v
)(
v
v
v
)(
v
)
=
(
v
v
)(
v
v
v
)
=
(
v
v
v
v
v
v
)
=
v
v
v
v
v
ДНФтуп.1(ƒ) =
v
v
v
=
v
v
v
ДНФтуп.2(ƒ) =
v
v
v
=
v
v
v
ДНФтуп.3(ƒ) =
v
v
v
=
v
v
v
ДНФтуп.4(ƒ) =
v
v
v
v
=
v
v
v
v
v
ДНФтуп.5(ƒ) =
v
v
v
=
v
v
v
r(ДНФтуп.1(ƒ)) = 11 =r(ДНФmin1(ƒ))
r(ДНФтуп.2(ƒ)) = 11 =r(ДНФmin2(ƒ))
r(ДНФтуп.3(ƒ)) = 11 =r(ДНФmin3(ƒ))
r(ДНФтуп.4(ƒ)) = 14
r(ДНФтуп.5(ƒ)) = 11 =r(ДНФmin4(ƒ))
ДНФтуп.1(ƒ) = ДНФmin1(ƒ)
ДНФтуп.2(ƒ) = ДНФmin2(ƒ)
ДНФтуп.3(ƒ) = ДНФmin3(ƒ)
ДНФтуп.5(ƒ) = ДНФmin4(ƒ)
Метод Квайна
|
|
|
|
|
|
|
0100 |
010- -100 |
-10-* -10- |
|
|
0011 0101 1010 1100 |
0-11* -011* 01-1* -101 101-* 1-10* 110- 11-0* |
|
|
|
0111 1011 1101 1110 |
|
|
v
v
v
v
v
v
v
r(ДНФсокр. (ƒ)) = 20
|
Дсокр.
|
0011 |
0100* |
0101 |
0111 |
1010 |
1011 |
1100 |
1101* |
1110 |
|
Я -10- |
|
⊕ |
+ |
|
|
|
+ |
⊕ |
|
|
0-11 |
+ |
|
|
+ |
|
|
|
|
|
|
-011 |
+ |
|
|
|
|
+ |
|
|
|
|
01-1 |
|
|
+ |
+ |
|
|
|
|
|
|
101- |
|
|
|
|
+ |
+ |
|
|
|
|
1-10 |
|
|
|
|
+ |
|
|
|
+ |
|
11-0 |
|
|
|
|
|
|
+ |
|
+ |
ДНФядр.(ƒ)
=
≠ ƒ
P = (
v
)
(
v
)(
v
)(
v
)(
v
)
(
v
)(
v
)
=
=
(
v
v
v
)(
v
v
v
)(
v
)
=
=
(
v
)(
v
v
v
)
=
(
v
v
v
v
v
v
)
=
v
v
v
v
ДНФтуп.1(ƒ)
=
v
v
v
=
v
v
v
ДНФтуп.2(ƒ)
=
v
v
v
=
v
v
v
ДНФтуп.3(ƒ)
=
v
v
v
=
v
v
v
ДНФтуп.4(ƒ)
=
v
v
v
=
v
v
v
ДНФтуп.5(ƒ)
=
v
v
v
v
=
v
v
v
v
r(ДНФтуп.1(ƒ)) = 11 =r(ДНФmin1(ƒ))
r(ДНФтуп.2(ƒ)) = 11 =r(ДНФmin2(ƒ))
r(ДНФтуп.3(ƒ)) = 11 =r(ДНФmin3(ƒ))
r(ДНФтуп.4(ƒ)) = 11 =r(ДНФmin4(ƒ))
r(ДНФтуп.5(ƒ)) = 14
ДНФтуп.1(ƒ) = ДНФmin1(ƒ)
ДНФтуп.2(ƒ) = ДНФmin2(ƒ)
ДНФтуп.3(ƒ) = ДНФmin3(ƒ)
ДНФтуп.4(ƒ) = ДНФmin4(ƒ)