The new Sum of Products (SOP) expression you uploaded is:

$\overline{A}BC + A\overline{B}C + AB\overline{C} + ABC$

This is the same as the previous expression:

1. $\overline{A}BC$ → $m_3$ (binary 011)
2. $A\overline{B}C$ → $m_5$ (binary 101)
3. $AB\overline{C}$ → $m_6$ (binary 110)
4. $ABC$ → $m_7$ (binary 111)

Let's map this onto the Karnaugh map (K-map) again. Since the expression is unchanged from before, we will get the same K-map result as previously outlined.

K-map Setup

Here’s the filled K-map for the expression:

Next Step: Simplifying using K-map Grouping

From the K-map, we can see that we have four ones. To simplify, we group the 1s to find a minimal Boolean expression.

1. Group 1: $m_3$ (011) and $m_7$ (111) can be grouped together vertically. This simplifies to $BC$.
2. Group 2: $m_5$ (101) and $m_7$ (111) can be grouped together horizontally. This simplifies to $AC$.

Thus, the simplified expression is: $BC + AC$

Let me know if you'd like further steps or have any questions.

Follow-up questions:

1. Would you like a step-by-step explanation on how the grouping was done?
2. Should I simplify a more complex expression involving four or more variables?
3. Do you want to see how this simplified expression can reduce the hardware requirements in digital logic?
4. Would you like to see another example with different minterms?
5. Do you need help with another type of Boolean simplification method (like Quine-McCluskey)?

Tip: When simplifying using a K-map, always look for the