Behavior of a 4-input OR gate: if exactly one input is HIGH (logic 1) and the other three inputs are LOW (logic 0), what is the gate's output?
Electronics and Communication Engineering
Digital Electronics
Difficulty: Easy
Choose an option
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Ais low
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Bis high
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Cis alternately high and low
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Dmay be high or low depending on relative magnitude of inputs
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Eis undefined
Answer
Correct Answer: is high
Explanation
Introduction / Context:Understanding the fundamental behavior of basic logic gates is essential for digital circuit design. The OR gate outputs a logic HIGH when any one (or more) of its inputs is HIGH. This problem reinforces that truth-table definition for a multi-input OR gate.
Given Data / Assumptions:
- Gate type: 4-input OR.
- Inputs: exactly one input = 1 (HIGH), the remaining three = 0 (LOW).
- Standard ideal logic levels are assumed (no analog threshold ambiguity).
Concept / Approach:The Boolean expression for a 4-input OR is Y = A + B + C + D, where + denotes the logical OR. The output is 1 if any operand is 1. This is independent of which particular input is HIGH; the logical outcome remains the same.
Step-by-Step Solution:
Let A = 1 and B = C = D = 0 (without loss of generality).Compute Y = A + B + C + D = 1 + 0 + 0 + 0 = 1.Therefore, the gate's output is HIGH.Verification / Alternative check:
Truth table for OR confirms that any single HIGH input is sufficient for a HIGH output. If more inputs become HIGH, the output remains HIGH.Why Other Options Are Wrong:
'is low': contradicts the OR definition.'alternately high and low': implies oscillation or metastability, not relevant here.'may be high or low depending on magnitude': applies to analog comparators, not ideal digital logic.'is undefined': applies to tri-states or unconnected inputs, not this case.Common Pitfalls:
Confusing OR (any input 1) with AND (all inputs 1) or XOR (odd number of 1s).Final Answer:
is high