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Основ=
;ные
логические
элементы<=
/b>
 =
;
Дискретный
преобразовk=
2;тель,
который
после
обработки
входных дво
=
80;чных
сигналов
выдаёт на
выходе
сигнал, явля=
102;щийся
значением
одной из
логических
операций,
называется логи&=
#1095;еским
элементом. =
Н=
1080;же
приведены
условные
обозначениn=
3;
(схемы)
базовых
логических
элементов,
реализующиm=
3;
логическое
умножение (конъюнкт
=
86;р),
логическое
сложение (дизъюнктор<=
/span>)
и отрицание
(инвертор).
Рис. Ко=
;нъюнктор,
дизъюнкm=
0;ор
и инвертор=
&nb=
sp;
Устройства
компьютера
(сумматоры в
процессоре,
ячейки
памяти в
оперативноl=
1;
памяти и др.)
строятся на
основе
базовых
логических
элементов.
Базов=
;ые
логические
элементы
реализуют
рассмотренl=
5;ые
выше три
основные
логические
операции,=
·
Л
=
86;гический
элемент «И»-
логическое
умножение,=
·
Л
=
86;гический
элемент
«ИЛИ»-
логическое
сложение,=
·
Л
=
86;гический
элемент «НЕ&raq=
uo;
– инверсию.
Посколь=
;ку
любая
логическая
операция, мо=
078;ет
быть
представлеl=
5;а
в виде
комбинации
трех основн
=
99;х,
любые
устройства
компьютера,
позволяющиk=
7;
обработку
или хранени
=
77;
информации,
могут быть
собраны из
базовых лог
=
80;ческих
элементов
как из
кирпичиков.
Логичес=
;кие
элементы
компьютера
оперируют с
сигналами,
представляn=
2;щими
собой элект
=
88;ические
импульсы. Ес=
090;ь
импульс -
логическое
значение
сигнала 1, нет
импульса=
;-
значение 0. На
вход
логических
элементов п
=
86;ступают
сигналы –
аргументы, н=
072;
выходе появ
=
83;яются
сигнал-функ
=
94;ия.
Преобра=
;зование
сигнала
логическим
элементом
задается
таблицей
состояния,
которая
фактически
является
таблицей
истинности,
соответствm=
1;ющей
логической
функции.
Логич=
;еский
элемент «И».
На входm=
9; А и В
логическогl=
6;
элемента
последоватk=
7;льно
подаются
четыре пары
сигналов
различных
значений, на
выходу
получается
последоватk=
7;льность
из четырех
сигналов,
значения
которых
определяютl=
9;я
в соответст
=
74;ие
с таблицей
истинности
операции ло
=
75;ического
умножения.=
=
&nb=
sp; =
А (0,0,1,1)
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
F (0,0,0,1)
=
&nb=
sp; =
В (0,1,0,1)
Или
другое
изображениk=
7;.
=
&nb=
sp; =
А (0,0,1,1)
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
F (0,0,0,1)=
=
&nb=
sp; =
В
(0,1,0,1)
Логичес=
;кий
элемент h=
8;
- схем
=
72; СОВПАДЕHИ=
071;
или КОНЪЮНКТО=
Р. Он
имеет два
входа и один
выход. Приме=
088;
электричесl=
2;ого
контура для
этого элеме
=
85;та:
Если
хотя бы на
одном из
входов буде
=
90;
0, т.е. конту=
;p
разомкнут, т=
086;
и на выходе
будет 0
(лампочка не
горит).
Едини=
;ца
на выходе
(лампочка
горит) тольк=
086;
в том случае,
когда на
обоих входа
=
93;
1 (контур замк&=
#1085;ут).
Логич=
;еский
элемент
«ИЛИ».
На входm=
9; А и В
логическогl=
6;
элемента
последоватk=
7;льно
подаются
четыре пары
сигналов
различных
значений, на
выходе
получается
последоватk=
7;льность
из четырех
сигналов,
значения ко
=
90;орых
определяютl=
9;я
в
соответствl=
0;е
с таблицей
истинности
операции
логическогl=
6;
сложения.=
<=
/p>
=
&nb=
sp;
А(0,0,1,1)
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
F (0,1,1,1)=
=
&nb=
sp; В(0,1,0,1)
Или
другое
изображениk=
7;.
=
&nb=
sp;
А(0,0,1,1)
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
F (0,1,1,1)=
=
&nb=
sp;
В(0,1,0,1)
Логичес=
;кий
элемент ИЛИ
называют СОБИРАТЕЛ
=
68;НОЙ
СХЕМОЙ или ДИh=
7;ЪЮНКТОРОМ.
Он имеет 2
входа
и 1 выход.
Работа элем
=
77;нта
ИЛИ
предполагаk=
7;т,
что сигнал 1
на входе
будет получ
=
77;н,
если сигнал 1
поступает
хотя бы на од=
1080;н
вход. Сигнал 0
на выходе
будет тольк
=
86;
в том случае,
если сигнал 1
не поступае
=
90;
ни на один из
входов.
Электричесl=
2;ий
контур в это=
084;
случае тако
=
74;:
<=
/p>
Если
хотя бы на
одном из
входов буде
=
90;
1, то конту<=
span
class=3DGramE>p будет
замкнут и на
выходе буде
=
90;
1 (лампочка горит=
;).
Логич=
;еский
элемент «НЕ&raq=
uo;.
На вход А
логическогl=
6;
элемента
последоватk=
7;льно
подаются дв
=
72;
сигнала, на
выходе
получается
=
87;оследовате=
1083;ьность
из двух
сигналов, зн=
072;чение
которых
определяютl=
9;я
в соответст
=
74;ии
с таблицей
истинности
логической
инверсии.=
<=
/p>
=
&nb=
sp;
А(0,1)  =
; &n=
bsp;  =
;
F(1,0)
Или
другое
изображениk=
7;.
<=
/p>
=
&nb=
sp;
А(0,1)  =
; &n=
bsp;  =
;
F(1,0)
Пр=
;остой
пример
инвертора -
электричесl=
2;ий
контур с
переключатk=
7;лем
и лампочкой.
При
замкнутом
переключатk=
7;ле
Х =3D 1, лампочка
гаснет, Z =
=3D 0.
При
разомкнутоl=
4;
переключатk=
7;ле
Х =3D 0, лампочка
горит, Z =3D 1.
=
o:p>
&nbs=
p;
Вычисли=
;тельные
схемы для
преобразовk=
2;ния
двоичных
кодов
строятся на =
080;х
элементарнm=
9;х
логических
элементах и
называются:
§ =
i=
7;УММАТОР – для
сложения
двоичных
кодов в А=
051;У
процессора
§ =
i=
6;ЕГИСТР
– длn=
3;
запоминаниn=
3;
двоичных
кодов в
памяти проц
=
77;ссора
§ =
i=
8;РИГГЕР – для
запоминаниn=
3;
двоичных
кодов в
оперативноl=
1;
памяти
Очень
часто
используютl=
9;я
комбинировk=
2;нные
логические
элементы,
сформироваl=
5;ные
из элементо
=
74;
«И» и «ИЛИ» с
отрицанием.
Они
называются
=
92;ункцией
Шеффера - «И-НЕ»
и функцией
Пирса «И
=
51;И-НЕ».
Они также
обладают
свойством
функционалn=
0;ной
полноты.
Фун=
кция
Шеффера
=
&nb=
sp;
А(0,0,1,1)
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
F (1,1,1,0)=
=
&nb=
sp;
В(0,1,0,1)
Фун=
кция
Пирса
А(0,0,1,1)
=
&nb=
sp; =
&nb=
sp;
=
&nb=
sp; =
F (0,0,0,1)=
=
&nb=
sp;
В(0,1,0,1)
Задания
для
самостоятеl=
3;ьного
выполнения=
1.
Существует 16
логических
функций от
двух
переменных
(смотри
таблицу 3.1). Пост=
роить
их
логические
схемы с помо=
097;ью
логических
элементов И, ИЛИ, НЕ.<=
/o:p>
2. &=
nbsp;
Доказать, чт=
086;
рассмотренl=
5;ая
в примере 3.11
логическая
схема
является
одноразрядl=
5;ым
двоичным
полусумматl=
6;ром
(не учитывае=
090;ся
перенос из
младшего
разряда).
3. &=
nbsp;
Доказать,
построив
таблицу ист
=
80;нности,
что логичес
=
82;ая
функция P =3D P =3D (
A
&
B
)Ú(
A
&
P
0)Ú(
B
&
P
0)
определяет
перенос в
старший
разряд при с=
083;ожении
двоичных
чисел (
A
и
B
- слагаемые, P
0 –
перенос из
младшего
разряда).
4. &=
nbsp;
Доказать,
построив
таблицу
истинности,
что
логическая
функция S =3D (
=
A
Ú
B<=
i> =
Ú
P 0)&
Ú(
A
&
B
&
P
0)
определяет
сумму при
сложении
двоичных чи
=
89;ел
(
A
и
B
- слагаемые, P
0 –
перенос из
младшего
разряда).
5. &=
nbsp;
Построить
логическую
схему
одноразрядl=
5;ого
двоичного
сумматора.=
6. &=
nbsp;
Какое
количество
базовых
логических
элементов
необходимо
для
реализации
64-разрядного
сумматора
двоичных
чисел.
7. &=
nbsp;
Какое
количество
базовых
логических =
01;лементов
составляют
оперативнуn=
2;
память
современноk=
5;о
компьютера
объемом 64 &=
#1052;байта.
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