The given Boolean expression is:

$Y = (\overline{A + \overline{B}})(\overline{B + C})(\overline{A + C})$

To convert this into Standard Product of Sums (POS) form, let's break down the process step-by-step.

Step 1: Apply De Morgan's Law

We'll first apply De Morgan's law to the terms where negations are outside parentheses. De Morgan's law states:

• $\overline{A + B} = \overline{A} \cdot \overline{B}$
• $\overline{A \cdot B} = \overline{A} + \overline{B}$

Let's apply it to each term:

1. $\overline{A + \overline{B}} = \overline{A} \cdot B$
2. $\overline{B + C} = \overline{B} \cdot \overline{C}$
3. $\overline{A + C} = \overline{A} \cdot \overline{C}$

So the expression becomes:

$Y = (\overline{A} \cdot B) (\overline{B} \cdot \overline{C}) (\overline{A} \cdot \overline{C})$

Step 2: Write the Expression in POS Form

The Product of Sums (POS) form means expressing the Boolean function as a product of sum terms, where each sum is an OR combination of literals. For this step, we aim to convert each product term into a sum by looking at the minimal form.

In this case, the original expression simplifies to a product, and this can already be seen as the product of individual terms. However, to strictly be in POS form, we look for maximal simplification of these sum terms.

Thus, the final POS form of the expression is:

$Y = (A + B)(B + C)(A + C)$

Conclusion:

The standard POS form for the given Boolean expression is: $Y = (A + B)(B + C)(A + C)$

Would you like further details or have any questions?

Here are some related questions:

1. What is the difference between SOP and POS forms in Boolean algebra?
2. How do De Morgan’s laws simplify complex Boolean expressions?
3. Can you provide an example of a Boolean function in SOP form and convert it to POS form?
4. What role do Boolean expressions play in digital logic design?
5. How can Boolean simplification techniques optimize hardware implementation?

Tip: Always double-check Boolean identities like De Morgan's laws when simplifying expressions, as small mistakes can lead to incorrect outcomes!