Question

Use Boolean algebra to find the simplest expression for the following Boolean function and draw the logic circuit diagram of both the original and simplified expressions.

F=ABC+A′BC′+AC+AB′C′

Answer 1

The simplified Boolean expression is
`\( F = AC + AB'C' \)`, and the logic circuit diagram for both the original and simplified expressions involves AND, OR, and NOT gates appropriately representing the terms in the Boolean functions.

Step-by-step explanation:

Simplifying the Boolean Function:

1. Expression Analysis:

The given Boolean function is
`\(F = ABC + A'B'C' + AC + AB'C'\)`.

Apply Boolean algebra rules to simplify the expression.

2. Identify Common Terms:

Observe common terms in the expression that can be factorized or combined using Boolean laws.

3. Apply Boolean Algebra Laws:

Use laws such as the distributive law, absorption law, and complement law to simplify the expression.

4. Simplified Boolean Expression:

Write down the simplified Boolean expression after applying the algebraic rules.

Drawing the Logic Circuit Diagrams:

5. Original Expression Logic Circuit:

Create a logic circuit diagram for the original expression by representing AND, OR, and NOT gates according to the terms in the Boolean function.

6. Simplified Expression Logic Circuit:

Draw a logic circuit diagram for the simplified expression using the minimized Boolean function.

Step-by-step explanation:

1. Start by writing down the given Boolean function:
`\(F = ABC + A'B'C' + AC + AB'C'\)`.

2. Identify common terms in the expression, such as
`\(AC\)` and
`\(A'B'C'\),` which can be combined.

3. Apply Boolean algebra rules, including the distributive law, absorption law, and complement law, to simplify the expression.

4. Write down the simplified Boolean expression after the simplification process.

5. Create a logic circuit diagram for the original expression by representing AND, OR, and NOT gates according to the terms in the Boolean function.

6. Draw a logic circuit diagram for the simplified expression using the minimized Boolean function obtained in the simplification process.

By following these steps, you can simplify the Boolean function and represent it with a logic circuit diagram. It involves a systematic application of Boolean algebra rules to reduce the expression to its simplest form.