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
Discussion & Comments