For the output of the following logic circuit to be '1', the values of inputs A and B should be respectively
Show Hint
A NOR gate outputs a 1 if and only if all of its inputs are completely clear (0). If even a single input is flipped to 1, the internal OR stage triggers, which turns the final inverted output into 0. Thus, 0 and 0 is the unique solution.
Step 1: Understanding the Question:
We are analyzing a logic gate circuit with two inputs, $A$ and $B$, and a final output $Y$. We need to find the specific input configuration that results in an output state of $Y = 1$.
Note: In this standard configuration, the logic assembly consists of a NOR gate layout (or an OR gate leading into a NOT gate inverter).
Step 2: Key Formula or Approach:
Let's track the Boolean logic operations through the circuit:
1. The first stage passes inputs $A$ and $B$ through an OR gate, yielding an intermediate expression: $X = A + B$.
2. The second stage passes this intermediate result through a NOT gate inverter to produce the final output: $Y = \overline{X} = \overline{A + B}$.
Step 3: Detailed Explanation:
We are given that the final desired output must be HIGH ($Y = 1$).
Substitute $Y = 1$ into our Boolean expression:
$$\overline{A + B} = 1$$
Taking the logical complement of both sides gives:
$$A + B = \overline{1} = 0$$
For the output of an OR operation ($A + B$) to equal $0$, every single individual input feeding into it must be strictly equal to $0$ simultaneously.
Therefore, we must have:
$$A = 0 \quad \text{and} \quad B = 0$$
Step 4: Final Answer:
The required values for inputs $A$ and $B$ are 0 and 0 respectively, which corresponds to option (B).
