To express the function $F(A, B, C, D) = \Sigma(0, 2, 5, 7, 10, 13)$ with eight or fewer literals, we need to minimize it using methods such as Karnaugh maps (K-maps) or Boolean algebra simplification. Here’s a step-by-step solution to finding three possible expressions.

Step 1: Identify the Minterms

The function $F(A, B, C, D)$ represents a sum of minterms:

• Minterms: 0, 2, 5, 7, 10, and 13.

Step 2: Construct the Karnaugh Map

Using a K-map for four variables (A, B, C, D) and placing the minterms, we can simplify the function.

K-Map Layout (AB for rows, CD for columns)

Step 3: Grouping Ones for Simplification

1. Group 1: Minterms 0 and 8 can be grouped together vertically, resulting in $\overline{A} \overline{B} \overline{D}$.
2. Group 2: Minterms 2 and 10 can be grouped, resulting in $\overline{A} C \overline{D}$.
3. Group 3: Minterms 5 and 7 can be grouped, resulting in $A \overline{C} D$.

These groups can be used to simplify the function expression.

Step 4: Simplified Expressions

Based on the grouping, here are three possible expressions for $F(A, B, C, D)$ with eight or fewer literals:

1. Expression 1: $F = \overline{A} \overline{B} \overline{D} + \overline{A} C \overline{D} + A \overline{C} D$
2. Expression 2: $F = \overline{A} \overline{B} \overline{D} + \overline{A} C \overline{D} + B D$
3. Expression 3: $F = A \overline{C} D + \overline{A} B \overline{D} + C \overline{B}$

Each of these expressions is minimized to use eight or fewer literals.

Would you like further details on any specific part, or have any additional questions?

Here are some related questions to deepen your understanding:

1. What is the importance of minimizing Boolean expressions in digital logic design?
2. How would the simplification differ if additional don't-care conditions were present?
3. What other methods, aside from Karnaugh maps, can be used to simplify Boolean functions?
4. How does the Karnaugh map technique help in reducing the number of gates in a circuit?
5. Can we use De Morgan's laws to further simplify the given expressions?

Tip: When simplifying Boolean functions, grouping in Karnaugh maps should cover the largest possible power-of-two groupings to achieve the minimal form.