Question

For each of the following fill up the truth table:

a) SOP Expression: AˉB+AB Cˉ+ AˉBCˉ+ABˉC
b) POS Expression: (Aˉ+B)(A+B+C)(A+B+C)

A B C X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Answer 1

The question involves filling out a truth table for given SOP and POS expressions. The truth table lists the values for all combinations of the binary variables A, B, and C. The filled truth table shows the results of evaluating the expressions for each combination.

Step-by-step explanation:

The question is asking to fill up a truth table for both the Sum of Products (SOP) and Product of Sums (POS) expressions given. We will evaluate each expression for every combination of the Boolean variables A, B, and C. Below is the filled truth table based on the given expressions:

• For A = 0, B = 0, C = 0: SOP = 0, POS = 1
• For A = 0, B = 0, C = 1: SOP = 0, POS = 0
• For A = 0, B = 1, C = 0: SOP = 0, POS = 0
• For A = 0, B = 1, C = 1: SOP = 1, POS = 0
• For A = 1, B = 0, C = 0: SOP = 0, POS = 0
• For A = 1, B = 0, C = 1: SOP = 1, POS = 0
• For A = 1, B = 1, C = 0: SOP = 1, POS = 0
• For A = 1, B = 1, C = 1: SOP = 1, POS = 0

Please note that the step-by-step calculations for each combination are not included but are essential in filling out the table accurately.