Inverse of an OR gate Which logic gate produces an output that is the exact logical inverse of the OR gate for all input combinations?

Introduction / Context:Identifying functional complements helps when replacing multi-gate structures with single universal gates, simplifying designs, and predicting the effect of bubbles (inversions) on schematics.

Given Data / Assumptions:

• We compare complete input–output truth tables.
• Standard positive logic is assumed.
• “Exact inverse” means output is the logical NOT of the OR output for every row.

Concept / Approach:

An OR gate implements Y = A + B + ... . The exact inverse is Y = (A + B + ...)’ which by definition is the NOR function. NOR is thus the complementary operation to OR across all input combinations.

Step-by-Step Solution:

Verification / Alternative check:

Truth tables: OR outputs 1 except for the all-zero input; NOR outputs 1 only for the all-zero input. Every row is complemented, confirming NOR is the inverse of OR.

Why Other Options Are Wrong:

• NOT is a single-input inverter, not the inverse of a multi-input OR function.
• NAND is the inverse of AND, not OR.
• AND and XOR are unrelated to being the full complement of OR.

Common Pitfalls:

• Confusing NOR with NAND. Use DeMorgan’s identities to keep complements straight.

Final Answer:

NOR