Question

Which of the following gates will give an output '1' for the given inputs?

• A. II and III
• B. I and IV
• C. I and III
• D. II and IV

Hint:

Remember the unique identifying properties for quick filter checks: a NOR gate is the only gate that outputs '1' when all inputs are completely low ('0'). An XOR gate outputs '1' whenever the input pair is unmatched. This lets you select option (D) rapidly!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given a set of logic gate diagrams with specific binary inputs applied to each. We need to evaluate the boolean behavior of each gate configuration to find which ones produce a high output state ('1').

Step 2: Key Formula or Approach:
We apply the standard truth definitions for common logic gates: NAND gate: Outputs '0' only when both inputs are '1'. NOR gate: Outputs '1' only when both inputs are '0'. AND gate: Outputs '1' only when both inputs are '1'. XOR gate: Outputs '1' when the inputs are different.

Step 3: Detailed Explanation:
Let's analyze the input and output conditions for each gate configuration shown in standard exam variants of this problem:

Gate I (NAND): Inputs are $(1, 1)$. The AND operation gives $1 \cdot 1 = 1$. Inverting this yields an output of $\sim 1 = 0$.

Gate II (NOR): Inputs are $(0, 0)$. The OR operation gives $0 + 0 = 0$. Inverting this yields an output of $\sim 0 = 1$.

Gate III (AND): Inputs are $(0, 1)$. The AND operation gives $0 \cdot 1 = 0$.

Gate IV (XOR): Inputs are $(1, 0)$. Since the two input signals are different, the XOR gate outputs a high state, $1$. Comparing our results, configurations II and IV both output a high state ('1').

Step 4: Final Answer:
The configurations that give an output '1' are II and IV, which corresponds to option (D).