Question

5) Постройте логические схемы для следующих функций: 1) F = (A & B & C) vB & CvA; (2) F = BV (C & A) V (A & B). ​

Answer 1

Ответ:

1. скрин 1 - F = (A & B & C) ∨ B & C ∨ A

2. скрин 2 - F = B ∨ (C & A) ∨ (A & B)

Объяснение:

Построение логических схем:

1) найти число логических переменных

2) найти количество основных логических операций и их порядок

3) нарисовать для каждой логической операции соответствующий ей элемент (скрин 3)

4) соединить элементы в порядке выполнения логических операций

1. F = (A & B & C) ∨ B & C ∨ A

1) 3 логические переменные - A, B и C

2) 5 логических операций:

1. A & B
2. A & B & C
3. B & C
4. (A & B & C) ∨ B & C
5. (A & B & C) ∨ B & C ∨ A

2. F = B ∨ (C & A) ∨ (A & B)

1) 3 логические переменные - A, B и C

2) 4 логических операций:

1. C & A
2. A & B
3. B ∨ (C & A)
4. B ∨ (C & A) ∨ (A & B)

Answer 2

Logical Circuit for Function F1

The logical function F1 is defined as F = (A & B & C) v (B & C v A).

To build a logical circuit for this function, we can break it down into smaller components and then combine them.

1. The first component is the AND gate (A & B & C). This gate takes three inputs (A, B, and C) and produces an output that is true (1) only when all three inputs are true (1).

2. The second component is the OR gate (B & C v A). This gate takes three inputs (B & C, A) and produces an output that is true (1) when either (B & C) or A is true (1).

3. Finally, we combine the outputs of the two components using another OR gate. This gate takes two inputs (output of the first component, output of the second component) and produces the final output of the function F.

Here is the logical circuit for function F1:

          +---[AND]---+
          |           |
    A ----|           |
          |           +---[OR]--- F
    B ----|           |
          |           |
    C ----|           |
          +---[AND]---+

Logical Circuit for Function F2

The logical function F2 is defined as F = BV (C & A) V (A & B).

To build a logical circuit for this function, we can follow a similar approach as before.

1. The first component is the AND gate (C & A). This gate takes two inputs (C and A) and produces an output that is true (1) only when both inputs are true (1).

2. The second component is the AND gate (A & B). This gate takes two inputs (A and B) and produces an output that is true (1) only when both inputs are true (1).

3. The third component is the OR gate. This gate takes two inputs (output of the first component, output of the second component) and produces the final output of the function F.

Here is the logical circuit for function F2:

          +---[AND]---+
          |           |
    C ----|           |
          |           +---[OR]--- F
    A ----|           |
          |           |
    B ----|           |
          +---[AND]---+

Please note that the logical circuits provided above are simplified representations of the given logical functions. The actual implementation may vary depending on the available logic gates and their configurations.