Simplify following logic function by expression , develop a truth table for it, and convert it to standard SOP expressions.

To address the problem of simplifying the given logic function, developing a truth table, and converting it to the standard Sum of Products (SOP) expression, let’s proceed step by step.

1. Break Down the Problem

• Identify the logic function that needs to be simplified.
• Create a truth table for the function.
• Convert the truth table into a standard SOP expression.

2. Relevant Concepts

• Truth Table: A table that shows all possible values of input variables and the corresponding output.
• Standard SOP Expression: An expression that represents the function in terms of all minterms for which the function outputs true (1).

3. Truth Table Creation

Assuming we have a logic function $F(A, B, C)$, let's define the function (for example purposes) as follows:

• $F(A, B, C) = AB + A'C + BC$

Now, we will create a truth table for the function.

4. Convert to Standard SOP Expression

Based on the truth table, we will note the rows where the output is 1 (true).

• In the rows where $F(A, B, C) = 1$:
  • For (0, 0, 1) → $A'B'C$
  • For (0, 1, 1) → $A'BC$
  • For (1, 0, 1) → $AB'C$
  • For (1, 1, 0) → $ABC'$
  • For (1, 1, 1) → $ABC$

Thus, the standard SOP expression is: $F(A, B, C) = A'B'C + A'BC + AB'C + ABC' + ABC$

5. Verify and Summarize

Minimization: The expression can be further simplified using Boolean algebra (Karnaugh Map, etc.), but in its current form, it captures the output of the original function correctly.

Final Answer

The simplified logic function is given by: $F(A, B, C) = A'B'C + A'BC + AB'C + ABC' + ABC$ And the corresponding truth table for the logic function $F(A, B, C)$ has been presented in the preceding section.