Question

Запишите логическую функцию с использованием условных обозначений алгебры-логики. Составьте схему и таблицу значений логической функции: Y=х1 и х2 или х3 или не х4

Answer 1

$Y=x_1\land x_2\lor x_3\lor\lnot x_4$
Таблица истинности и функциональная схема приведены во вложениях.

Answer 2

Logical Function and Truth Table

The logical function given is: Y = x1 AND x2 OR x3 OR NOT x4.

To create a truth table for this logical function, we need to consider all possible combinations of the input variables x1, x2, x3, and x4. There are 2^4 = 16 possible combinations.

Here is the truth table for the logical function:

| x1 | x2 | x3 | x4 | Y | |----|----|----|----|---| | 0 | 0 | 0 | 0 | 1 | | 0 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 0 | 1 | | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 1 | 0 | | 1 | 0 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 |

Logical Function Circuit Diagram

To represent the logical function using circuit symbols, we can use AND, OR, and NOT gates. Here is the circuit diagram for the given logical function:

     +-----+
x1 --|     |
     | AND +----+
x2 --|     |    |
     +-----+    |
                |
x3 ------------+
                |
x4 ------------+
                |
     +-----+    |
     | NOT +----+
     +-----+

In the circuit diagram, the AND gate represents the logical AND operation, the OR gate represents the logical OR operation, and the NOT gate represents the logical NOT operation.

Conclusion

In conclusion, the logical function Y = x1 AND x2 OR x3 OR NOT x4 can be represented using a truth table and a circuit diagram. The truth table shows the output Y for all possible combinations of the input variables x1, x2, x3, and x4. The circuit diagram represents the logical function using AND, OR, and NOT gates.