Question

For the logic circuit shown, the truth table is :

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is A

To determine the truth table of the given logic circuit, we need to analyze the circuit step-by-step.

The circuit consists of: 

• Two NOT gates receiving inputs A and B.
• An OR gate taking the outputs of the NOT gates as inputs.
• A final NOT gate after the OR gate resulting in output Y.

Let's break down the steps:

1. The inputs are A and B.
2. The NOT gates invert these inputs, producing \(\overline{A}\) and \(\overline{B}\).
3. The OR gate outputs \(\overline{A} + \overline{B}\).
4. The final NOT gate inverts the output of the OR gate to produce Y, which is \(\overline{\overline{A} + \overline{B}}\).

The final expression \(\overline{\overline{A} + \overline{B}}\) represents the logical NAND operation, which states \(A \cdot B\) when expanded using De Morgan's laws.

A	B	\(\overline{A}\)	\(\overline{B}\)	\(\overline{A} + \overline{B}\)	Y
0	0	1	1	1	0
0	1	1	0	1	0
1	0	0	1	1	0
1	1	0	0	0	1

Based on the truth table, the correct answer matches the option with the following outcomes:

Hence, the truth table of the circuit corresponds to the NAND logic, and the correct answer is the option provided above.