In signal-level conventions, a positive-logic AND gate is equivalent to which negative-logic gate (i.e., when 0 and 1 meanings are swapped for inputs and output)?

Introduction / Context:Logic functions depend not only on gate symbols but also on the interpretation of voltage levels. Under positive logic, high = 1 and low = 0. Under negative logic, this interpretation is inverted. Understanding equivalence between positive- and negative-logic gates is a classic application of De Morgan’s transformations and level conventions.

Given Data / Assumptions:

• Positive logic: high means 1, low means 0.
• Negative logic: high means 0, low means 1 (polarity inverted).
• We seek the negative-logic gate that performs the same Boolean relation as a positive-logic AND.

Concept / Approach:

When signal interpretation flips, the logical operations dualize. A positive-logic AND corresponds to a negative-logic OR: both represent the same underlying hardware relation viewed through opposite level meanings. Intuitively, if asserting any negative-logic input (i.e., pulling it low in physical voltage) suffices to assert the output (also low), then in negative-logic terms the function is OR while in positive-logic terms the same hardware is AND.

Step-by-Step Solution:

Verification / Alternative check:

Apply De Morgan’s view of complemented variables and observe that complementing inputs and output of OR yields AND and vice versa when switching logic sense.

Why Other Options Are Wrong:

NAND/NOR involve output inversion relative to AND/OR, which is not what a pure logic-sense swap implies. 'AND gate' does not change with a polarity swap. Thus 'OR gate' is the correct negative-logic equivalent.

Common Pitfalls:

Confusing negative logic (level interpretation) with inserting physical inverters, and mixing up NAND/NOR identities with logic-sense equivalence.

Final Answer:

OR gate