Positive vs negative logic equivalence: Which positive-logic function is equivalent to the OR function when interpreted in negative logic?

Introduction / Context:
Logic families sometimes use negative logic, where logical 1 is represented by a low voltage and logical 0 by a high voltage. Understanding how operations translate between positive and negative logic is crucial for interpreting mixed-signal documentation and designing with active-low signals.

Given Data / Assumptions:

• Positive logic: 1 = high, 0 = low.
• Negative logic: 1 = low, 0 = high (signal meanings are inverted).
• We seek the positive-logic function equivalent to OR under negative-logic interpretation.

Concept / Approach:
Using De Morgan’s transformations with signal complementation: an OR operation on active-low (negative logic) signals corresponds to an AND operation on their positive-logic complements. Intuitively, when low means asserted, combining two asserted-lows with OR (in the active-low sense) becomes an AND of their true (active-high) intents.

Step-by-Step Solution:
Let X̄ and Ȳ be active-low signals whose positive-logic meanings are X and Y.Negative-logic OR: X̄ OR Ȳ (low means true) corresponds to NOT( (NOT X) AND (NOT Y) ) in positive logic.Equivalently, the underlying positive-logic operation combining the true conditions is X AND Y.Thus, OR in negative logic ↔ AND in positive logic.

Verification / Alternative check:
Truth table mapping: when either X̄ or Ȳ is low (meaning X or Y is true), the combined condition holds exactly when X AND Y is the corresponding positive-logic combination for asserting active-low outputs. Formal De Morgan rules confirm this equivalence.

Why Other Options Are Wrong:
NOT and NOR do not capture the duality between OR under negative logic and positive-logic AND. Choosing OR ignores the change in signal polarity that flips the operator.

Common Pitfalls:
Forgetting that both signal levels and operators transform under negative logic; applying De Morgan to signals but not to the operator, or vice versa.

Final Answer:
AND