Introduction:
The prompt describes an output that is HIGH exclusively when both inputs are HIGH, and LOW otherwise. Recognizing this verbal truth table is a core skill in digital electronics for mapping behaviors to gate names.
Given Data / Assumptions:
- Inputs: A and B are binary (LOW = 0, HIGH = 1)
- Output: X is binary
- X is HIGH only if A = 1 and B = 1
Concept / Approach:
The AND function outputs 1 only when all inputs are 1. If any input is 0, the output is 0. This statement precisely matches the verbal rule provided.
Step-by-Step Solution:
Step 1: Translate text to logic: X = 1 only when A = 1 and B = 1.Step 2: Standard AND truth table: 00 → 0, 01 → 0, 10 → 0, 11 → 1.Step 3: The rule matches the AND truth table exactly.
Verification / Alternative check:
Compare to OR: OR would output 1 when any input is 1, which contradicts the prompt. XOR outputs 1 when inputs differ, also not matching. NAND outputs 0 only for 11, which is the inverse of the described behavior.
Why Other Options Are Wrong:
XOR gate: High for unequal inputs, not both high.OR gate: High if any input is high; contradicts rule for single highs.NAND gate: Inverts AND; output would be LOW when both inputs are HIGH.
Common Pitfalls:
Misreading the phrase "or both are LOW" as an OR description; the key is output LOW in those cases.Confusing NAND with AND due to similar names.
Final Answer:
AND gate
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