Question

Identify the correct truth table of the given logic circuit. 

• A. A
• B. B
• C. C
• D. D

Hint:

Always reduce complex logic circuits into Boolean expressions before drawing the truth table.

Answer 1

The Correct Option is B

To solve the problem of identifying the correct truth table for the given logic circuit, let's analyze each logical gate step-by-step.

The logic circuit involves the following:

• The first gate is an AND gate receiving inputs A and B.
• The second gate is a NOT gate inverting the output of the first gate.
• The third gate is another AND gate that combines the output of the NOT gate with the original input A.
• The final gate is an OR gate that produces the output Y.

Now let's compute the output step-by-step:

1. Calculate the output of the first AND gate: \(C = A \cdot B\)
2. Apply the NOT gate: \(C' = \overline{C}\)
3. Calculate the output of the second AND gate: \(D = A \cdot C'\)
4. Apply the OR gate: \(Y = C + D\)

Let's create a truth table based on these calculations:

A	B	C = A . B	C'	D = A . C'	Y = C + D
0	0	0	1	0	0
0	1	0	1	0	1
1	0	0	1	1	1
1	1	1	0	0	1

Analyzing our derived truth table, we can find the correct answer:

The correct truth table corresponds to option B from the provided choices.