3.2.1. Минимальные суммы
Одна из мер сложности булевых выражений определяется числом букв, входящих в выражение, то есть числом переменных и их инверсий. Переменные и их инверсии – литералы. Выражения в форме суммы произведений с минимальным числом литералов – минимальные суммы.
При выборе групп, дающих минимальную сумму, руководствуются следующими двумя принципами:
– группа должна быть как можно больше;
– групп должно быть как можно меньше.
Чтобы написать выражение по карте Карно, нужно воспользоваться «разметкой» координатных осей карты. Нужно для каждой группы отобрать те переменные на координатных осях, чьи значения не изменяются в пределах группы. Эти переменные и будут входить в соответствующие термы-произведения. Если переменные равны логическому нулю, то они должны входить с отрицанием, если равны логической единице – без отрицания.
С точки зрения формирования прямоугольных групп карту нужно считать трехмерной (для 3-х переменных – карта как цилиндр со склеенными правым и левым краями).
Пример 8 Определим минимальные суммы по карте Карно
|
|
|
YZ | |||
|
|
|
00 |
01 |
11 |
10 |
|
WX |
00 |
1 |
0 |
1 |
1 |
|
01 |
1 |
0 |
1 |
1 | |
|
11 |
1 |
1 |
0 |
0 | |
|
10 |
1 |
0 |
0 |
0 | |
Y=1, Z меняет знак (1→0),
W=0 – входит с отрицанием,
X меняет знак (0→1)
,
Z
меняет знак (0→1)
,
X
и W
меняют знак
.
3.2.2. Минимальные произведения
Для получения минимального произведения нужно обратиться к тем ячейкам карты Карно, в которых находятся нули. Затем нужно взять отрицание полученной суммы произведений, воспользовавшись законом де Моргана.
Пример 9 Определим минимальные произведения по карте Карно
|
|
|
YZ | |||
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|
00 |
01 |
11 |
10 |
|
WX |
00 |
1 |
1 |
0 |
1 |
|
01 |
0 |
0 |
0 |
0 | |
|
11 |
0 |
0 |
0 |
1 | |
|
10 |
1 |
1 |
0 |
1 | |
Y, Z меняют знак ,
W=0 – входит с отрицанием, X=1
,
W
и X
меняют знак
,
X
и W
меняют знак
.
3.2.3. Недоопределенные условия
В некоторых случаях известно, что какие-то комбинации на входе появиться не могут, или же, если они появляются, то значение на выходе не существенно. Для таких ситуаций нет необходимости определять выходные значения схемы, то есть значения функции в таблице истинности − недоопределенные условия.
Любую из таких ячеек можно включать как в группу единичных, так и в группу нулевых ячеек или вообще никуда не включать.
3.3. Задания к практическому занятию
1. Постройте таблицы истинности для заданных булевых функций.
2. Составьте канонические суммы минтермов для таблиц истинности.
3. Получите отрицание заданных выражений.
4. Получите канонические произведения макстермов по таблицам истинности.
5. Постройте минимальные суммы и минимальные произведения по картам Карно.
|
|
Вариант 1 |
Вариант 2 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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1.1)
|
2.1)
| ||||||||||||
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1.2) |
X |
Y |
Z |
F |
|
2.2) |
X |
Y |
Z |
F |
| |||
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0 |
0 |
0 |
0 |
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0 |
0 |
0 |
1 |
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0 |
0 |
1 |
1 |
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0 |
0 |
1 |
0 |
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0 |
1 |
0 |
1 |
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0 |
1 |
0 |
1 |
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0 |
1 |
1 |
0 |
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0 |
1 |
1 |
0 |
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1 |
0 |
0 |
0 |
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1 |
0 |
0 |
0 |
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1 |
0 |
1 |
0 |
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1 |
0 |
1 |
1 |
| |||
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1 |
1 |
0 |
1 |
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1 |
1 |
0 |
1 |
| |||
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1 |
1 |
1 |
0 |
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1 |
1 |
1 |
0 |
| |||
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1.3)
|
2.3)
| ||||||||||||
|
1.4) |
X |
Y |
Z |
F |
|
2.4) |
X |
Y |
Z |
F |
| |||
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0 |
0 |
0 |
0 |
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0 |
0 |
0 |
0 |
| |||
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0 |
0 |
1 |
0 |
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0 |
0 |
1 |
0 |
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0 |
1 |
0 |
0 |
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0 |
1 |
0 |
1 |
| |||
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0 |
1 |
1 |
1 |
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0 |
1 |
1 |
1 |
| |||
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1 |
0 |
0 |
1 |
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1 |
0 |
0 |
0 |
| |||
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1 |
0 |
1 |
1 |
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1 |
0 |
1 |
0 |
| |||
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1 |
1 |
0 |
0 |
|
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1 |
1 |
0 |
1 |
| |||
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1 |
1 |
1 |
0 |
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1 |
1 |
1 |
1 |
| |||
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| |||||||||
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1.5) |
XY |
|
2.5) |
XY |
| |||||||||
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00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
1 |
1 |
1 |
|
00 |
1 |
1 |
1 |
0 |
| |||
|
WZ 01 |
0 |
0 |
1 |
1 |
|
WZ 01 |
0 |
1 |
1 |
0 |
| |||
|
11 |
0 |
0 |
1 |
0 |
|
11 |
0 |
1 |
0 |
0 |
| |||
|
10 |
0 |
0 |
0 |
0 |
|
10 |
0 |
1 |
0 |
0 |
| |||
|
|
Вариант 3 |
Вариант 4 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
3.1)
|
4.1)
| ||||||||||||
|
3.2) |
X |
Y |
Z |
F |
|
4.2) |
X |
Y |
Z |
F |
| |||
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0 |
0 |
0 |
1 |
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0 |
0 |
0 |
0 |
| |||
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0 |
0 |
1 |
0 |
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0 |
0 |
1 |
1 |
| |||
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0 |
1 |
0 |
1 |
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0 |
1 |
0 |
0 |
| |||
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0 |
1 |
1 |
0 |
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0 |
1 |
1 |
1 |
| |||
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1 |
0 |
0 |
1 |
|
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1 |
0 |
0 |
0 |
| |||
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1 |
0 |
1 |
0 |
|
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1 |
0 |
1 |
1 |
| |||
|
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1 |
1 |
0 |
1 |
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|
1 |
1 |
0 |
1 |
| |||
|
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1 |
1 |
1 |
0 |
|
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1 |
1 |
1 |
0 |
| |||
|
|
3.3)
|
4.3)
| ||||||||||||
|
3.4) |
X |
Y |
Z |
F |
|
4.4) |
X |
Y |
Z |
F |
| |||
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0 |
0 |
0 |
1 |
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0 |
0 |
0 |
0 |
| |||
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0 |
0 |
1 |
1 |
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0 |
0 |
1 |
0 |
| |||
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0 |
1 |
0 |
0 |
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0 |
1 |
0 |
0 |
| |||
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0 |
1 |
1 |
0 |
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0 |
1 |
1 |
0 |
| |||
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1 |
0 |
0 |
0 |
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1 |
0 |
0 |
1 |
| |||
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1 |
0 |
1 |
0 |
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1 |
0 |
1 |
1 |
| |||
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1 |
1 |
0 |
1 |
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1 |
1 |
0 |
1 |
| |||
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1 |
1 |
1 |
1 |
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1 |
1 |
1 |
1 |
| |||
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| |||||||||
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3.5) |
XY |
|
4.5) |
XY |
| |||||||||
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00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
1 |
1 |
1 |
|
00 |
0 |
0 |
1 |
1 |
| |||
|
WZ 01 |
1 |
1 |
0 |
0 |
|
WZ 01 |
0 |
0 |
1 |
1 |
| |||
|
11 |
1 |
1 |
0 |
0 |
|
11 |
0 |
1 |
1 |
0 |
| |||
|
10 |
1 |
1 |
0 |
0 |
|
10 |
0 |
1 |
1 |
0 |
| |||
|
|
Вариант 5 |
Вариант 6 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
5.1а)
|
6.1)
| ||||||||||||
|
5.2) |
X |
Y |
Z |
F |
|
6.2) |
X |
Y |
Z |
F |
| |||
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0 |
0 |
0 |
0 |
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0 |
0 |
0 |
0 |
| |||
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0 |
0 |
1 |
1 |
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0 |
0 |
1 |
0 |
| |||
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0 |
1 |
0 |
1 |
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0 |
1 |
0 |
1 |
| |||
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0 |
1 |
1 |
0 |
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0 |
1 |
1 |
0 |
| |||
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1 |
0 |
0 |
0 |
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1 |
0 |
0 |
1 |
| |||
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1 |
0 |
1 |
0 |
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1 |
0 |
1 |
0 |
| |||
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1 |
1 |
0 |
0 |
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1 |
1 |
0 |
1 |
| |||
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1 |
1 |
1 |
1 |
|
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1 |
1 |
1 |
0 |
| |||
|
|
5.3)
|
6.3)
| ||||||||||||
|
5.4) |
X |
Y |
Z |
F |
|
6.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
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0 |
0 |
0 |
1 |
| |||
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0 |
0 |
1 |
1 |
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0 |
0 |
1 |
0 |
| |||
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0 |
1 |
0 |
0 |
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0 |
1 |
0 |
1 |
| |||
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0 |
1 |
1 |
1 |
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0 |
1 |
1 |
1 |
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1 |
0 |
0 |
1 |
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1 |
0 |
0 |
1 |
| |||
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1 |
0 |
1 |
0 |
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1 |
0 |
1 |
1 |
| |||
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1 |
1 |
0 |
0 |
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1 |
1 |
0 |
0 |
| |||
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1 |
1 |
1 |
1 |
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1 |
1 |
1 |
0 |
| |||
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| |||||||||
|
5.5) |
XY |
|
6.5) |
XY |
| |||||||||
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00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
0 |
0 |
1 |
1 |
|
00 |
0 |
0 |
1 |
0 |
| |||
|
WZ 01 |
0 |
0 |
1 |
1 |
|
WZ 01 |
0 |
0 |
1 |
0 |
| |||
|
11 |
1 |
1 |
0 |
0 |
|
11 |
1 |
1 |
1 |
1 |
| |||
|
10 |
1 |
1 |
0 |
0 |
|
10 |
0 |
0 |
1 |
1 |
| |||
|
|
Вариант 7 |
Вариант 8 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
7.1а)
|
8.1)
| ||||||||||||
|
7.2) |
X |
Y |
Z |
F |
|
8.2) |
X |
Y |
Z |
F |
| |||
|
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0 |
0 |
0 |
1 |
|
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0 |
0 |
0 |
0 |
| |||
|
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0 |
0 |
1 |
1 |
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0 |
0 |
1 |
0 |
| |||
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0 |
1 |
0 |
0 |
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0 |
1 |
0 |
1 |
| |||
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0 |
1 |
1 |
0 |
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0 |
1 |
1 |
1 |
| |||
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1 |
0 |
0 |
0 |
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1 |
0 |
0 |
1 |
| |||
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1 |
0 |
1 |
0 |
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1 |
0 |
1 |
0 |
| |||
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1 |
1 |
0 |
1 |
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1 |
1 |
0 |
0 |
| |||
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1 |
1 |
1 |
1 |
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1 |
1 |
1 |
0 |
| |||
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|
7.3)
|
8.3)
| ||||||||||||
|
7.4) |
X |
Y |
Z |
F |
|
8.4) |
X |
Y |
Z |
F |
| |||
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0 |
0 |
0 |
0 |
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0 |
0 |
0 |
0 |
| |||
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0 |
0 |
1 |
1 |
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0 |
0 |
1 |
0 |
| |||
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0 |
1 |
0 |
1 |
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0 |
1 |
0 |
1 |
| |||
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0 |
1 |
1 |
0 |
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0 |
1 |
1 |
1 |
| |||
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1 |
0 |
0 |
0 |
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1 |
0 |
0 |
0 |
| |||
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1 |
0 |
1 |
1 |
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1 |
0 |
1 |
0 |
| |||
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1 |
1 |
0 |
0 |
|
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1 |
1 |
0 |
1 |
| |||
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1 |
1 |
1 |
1 |
|
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1 |
1 |
1 |
1 |
| |||
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| |||||||||
|
7.5) |
XY |
|
8.5) |
XY |
| |||||||||
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00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
0 |
1 |
0 |
|
00 |
1 |
1 |
0 |
0 |
| |||
|
WZ 01 |
1 |
0 |
1 |
0 |
|
WZ 01 |
1 |
1 |
0 |
0 |
| |||
|
11 |
1 |
0 |
1 |
0 |
|
11 |
0 |
0 |
1 |
1 |
| |||
|
10 |
1 |
0 |
1 |
0 |
|
10 |
0 |
0 |
1 |
1 |
| |||
|
|
Вариант 9 |
Вариант 10 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
9.1а)
|
101)
| ||||||||||||
|
9.2) |
X |
Y |
Z |
F |
|
10.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
0 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
0 |
|
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1 |
0 |
0 |
1 |
| |||
|
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1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
1 |
| |||
|
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1 |
1 |
0 |
1 |
|
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1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
9.3)
|
10.3)
| ||||||||||||
|
9.4) |
X |
Y |
Z |
F |
|
10.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
0 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
1 |
| |||
|
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1 |
0 |
0 |
0 |
|
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1 |
0 |
0 |
1 |
| |||
|
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1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
|
|
|
|
| |||||||||
|
9.5) |
XY |
|
10.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
1 |
0 |
0 |
|
00 |
0 |
1 |
0 |
0 |
| |||
|
WZ 01 |
1 |
1 |
0 |
0 |
|
WZ 01 |
1 |
1 |
1 |
1 |
| |||
|
11 |
0 |
1 |
1 |
1 |
|
11 |
0 |
1 |
0 |
0 |
| |||
|
10 |
0 |
1 |
0 |
0 |
|
10 |
0 |
1 |
0 |
0 |
| |||
|
|
Вариант 11 |
Вариант 12 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
11.1а)
|
12.1)
| ||||||||||||
|
11.2) |
X |
Y |
Z |
F |
|
12.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
0 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
1 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
11.3)
|
12.3)
| ||||||||||||
|
11.4) |
X |
Y |
Z |
F |
|
12.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
0 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
|
|
|
|
| |||||||||
|
11.5) |
XY |
|
12.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
0 |
0 |
0 |
|
00 |
1 |
1 |
0 |
0 |
| |||
|
WZ 01 |
1 |
1 |
1 |
0 |
|
WZ 01 |
1 |
1 |
1 |
1 |
| |||
|
11 |
1 |
0 |
0 |
0 |
|
11 |
0 |
1 |
0 |
0 |
| |||
|
10 |
1 |
1 |
0 |
0 |
|
10 |
0 |
1 |
0 |
0 |
| |||
|
|
Вариант 13 |
Вариант 14 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
13.1а)
|
14.1)
| ||||||||||||
|
13.2) |
X |
Y |
Z |
F |
|
14.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
0 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
0 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
13.3)
|
14.3)
| ||||||||||||
|
13.4) |
X |
Y |
Z |
F |
|
14.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
0 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
1 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
|
|
|
|
| |||||||||
|
13.5) |
XY |
|
14.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
0 |
0 |
0 |
0 |
|
00 |
1 |
0 |
0 |
0 |
| |||
|
WZ 01 |
0 |
1 |
1 |
1 |
|
WZ 01 |
1 |
1 |
0 |
0 |
| |||
|
11 |
0 |
1 |
0 |
0 |
|
11 |
1 |
1 |
0 |
0 |
| |||
|
10 |
0 |
1 |
0 |
0 |
|
10 |
1 |
0 |
0 |
0 |
| |||
|
|
Вариант 15 |
Вариант 16 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
15.1а)
|
16.1)
| ||||||||||||
|
15.2) |
X |
Y |
Z |
F |
|
16.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
0 |
|
|
0 |
1 |
0 |
1 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
0 |
| |||
|
|
1 |
0 |
1 |
1 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
15.3)
|
16.3)
| ||||||||||||
|
15.4) |
X |
Y |
Z |
F |
|
16.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
1 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
0 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
|
|
|
|
| |||||||||
|
15.5) |
XY |
|
16.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
1 |
1 |
1 |
|
00 |
1 |
1 |
0 |
0 |
| |||
|
WZ 01 |
0 |
1 |
0 |
1 |
|
WZ 01 |
1 |
0 |
0 |
0 |
| |||
|
11 |
0 |
1 |
0 |
1 |
|
11 |
1 |
1 |
0 |
0 |
| |||
|
10 |
0 |
0 |
0 |
0 |
|
10 |
1 |
1 |
0 |
0 |
| |||
|
|
Вариант 17 |
Вариант 18 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
17.1а)
|
18.1)
| ||||||||||||
|
17.2) |
X |
Y |
Z |
F |
|
18.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
0 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
1 |
|
|
1 |
0 |
0 |
0 |
| |||
|
|
1 |
0 |
1 |
1 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
17.3)
|
18.3)
| ||||||||||||
|
17.4) |
X |
Y |
Z |
F |
|
18.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
1 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
|
|
|
|
| |||||||||
|
17.5) |
XY |
|
18.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
0 |
1 |
1 |
|
00 |
1 |
1 |
0 |
0 |
| |||
|
WZ 01 |
1 |
0 |
0 |
1 |
|
WZ 01 |
1 |
1 |
0 |
0 |
| |||
|
11 |
1 |
0 |
0 |
1 |
|
11 |
1 |
0 |
0 |
1 |
| |||
|
10 |
1 |
1 |
0 |
1 |
|
10 |
1 |
0 |
0 |
1 |
| |||
|
|
Вариант 19 |
Вариант 20 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
19.1а)
|
20.1)
| ||||||||||||
|
19.2) |
X |
Y |
Z |
F |
|
20.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
1 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
1 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
1 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
19.3)
|
20.3)
| ||||||||||||
|
19.4) |
X |
Y |
Z |
F |
|
20.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
0 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
|
|
|
|
| |||||||||
|
19.5) |
XY |
|
20.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
1 |
0 |
0 |
|
00 |
1 |
1 |
0 |
0 |
| |||
|
WZ 01 |
1 |
1 |
0 |
0 |
|
WZ 01 |
1 |
1 |
0 |
0 |
| |||
|
11 |
0 |
0 |
1 |
1 |
|
11 |
0 |
1 |
0 |
1 |
| |||
|
10 |
0 |
0 |
1 |
1 |
|
10 |
0 |
1 |
0 |
1 |
| |||
|
|
Вариант 21 |
Вариант 22 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
21.1а)
|
22.1)
| ||||||||||||
|
21.2) |
X |
Y |
Z |
F |
|
22.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
1 |
|
|
0 |
0 |
1 |
0 |
| |||
|
|
0 |
1 |
0 |
0 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
1 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
0 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
| |||
|
|
21.3)
|
22.3)
| ||||||||||||
|
21.4) |
X |
Y |
Z |
F |
|
22.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
0 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
1 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
|
|
|
|
| |||||||||
|
21.5) |
XY |
|
22.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
0 |
0 |
0 |
1 |
|
00 |
1 |
1 |
1 |
1 |
| |||
|
WZ 01 |
0 |
1 |
1 |
1 |
|
WZ 01 |
0 |
0 |
0 |
0 |
| |||
|
11 |
0 |
1 |
1 |
1 |
|
11 |
0 |
1 |
1 |
0 |
| |||
|
10 |
0 |
0 |
0 |
1 |
|
10 |
0 |
1 |
1 |
0 |
| |||
|
|
Вариант 23 |
Вариант 24 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
23.1а)
|
24.1)
| ||||||||||||
|
23.2) |
X |
Y |
Z |
F |
|
24.2) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
1 |
|
|
0 |
0 |
0 |
1 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
0 |
| |||
|
|
0 |
1 |
1 |
0 |
|
|
0 |
1 |
1 |
0 |
| |||
|
|
1 |
0 |
0 |
1 |
|
|
1 |
0 |
0 |
1 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
0 |
| |||
|
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
23.3)
|
24.3)
| ||||||||||||
|
23.4) |
X |
Y |
Z |
F |
|
24.4) |
X |
Y |
Z |
F |
| |||
|
|
0 |
0 |
0 |
0 |
|
|
0 |
0 |
0 |
0 |
| |||
|
|
0 |
0 |
1 |
0 |
|
|
0 |
0 |
1 |
1 |
| |||
|
|
0 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
1 |
| |||
|
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
1 |
| |||
|
|
1 |
0 |
0 |
0 |
|
|
1 |
0 |
0 |
0 |
| |||
|
|
1 |
0 |
1 |
0 |
|
|
1 |
0 |
1 |
0 |
| |||
|
|
1 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
1 |
| |||
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
1 |
0 |
| |||
|
|
|
|
|
|
| |||||||||
|
23.5) |
XY |
|
24.5) |
XY |
| |||||||||
|
|
00 |
01 |
11 |
10 |
|
|
00 |
01 |
11 |
10 |
| |||
|
00 |
1 |
0 |
1 |
1 |
|
00 |
1 |
1 |
0 |
0 |
| |||
|
WZ 01 |
1 |
0 |
0 |
1 |
|
WZ 01 |
1 |
1 |
0 |
0 |
| |||
|
11 |
1 |
0 |
0 |
1 |
|
11 |
0 |
1 |
1 |
0 |
| |||
|
10 |
1 |
1 |
0 |
1 |
|
10 |
0 |
1 |
0 |
0 |
| |||
