Applying De Morgan’s law, what overall logic function results from inverting each input of an AND gate (inputs only, output not inverted)?

Introduction / Context:
Transforming logic by adding input inverters is a fundamental technique in gate-level design. De Morgan’s laws provide the algebraic toolset to predict the resulting function without exhaustive truth tables. Here we start with an AND gate and invert each input before it reaches the gate, while leaving the output unchanged.

Given Data / Assumptions:

• Base gate: AND with inputs A, B, ...
• Each input is inverted prior to the AND stage.
• No inversion on the output node.

Concept / Approach:

Let A' = NOT A and B' = NOT B. The gate computes F = A' AND B'. By De Morgan’s law, (NOT A) AND (NOT B) = NOT (A OR B). This definition is precisely the NOR function of the original (non-inverted) variables. Thus, input inversion around an AND gate implements NOR overall.

Step-by-Step Solution:

Verification / Alternative check:

Truth-table enumeration for two inputs confirms that F = 1 only when A = 0 and B = 0, matching NOR.

Why Other Options Are Wrong:

OR requires output inversion as well. NAND results from inverting only the output of AND. XOR is unrelated to De Morgan’s complement-of-sum relation.

Common Pitfalls:

Forgetting whether the output is inverted, and mixing up the two De Morgan identities (complement of product vs complement of sum).

Final Answer:

NOR