According to De Morgan’s theorems in digital logic, a NAND gate is functionally equivalent to which bubbled logic gate representation?

Introduction / Context:
De Morgan’s theorems allow the transformation of logic networks by moving inversions between inputs and outputs. Understanding the 'bubbled' gate notation helps designers substitute equivalent forms for simplification and implementation with available hardware.

Given Data / Assumptions:

• NAND = NOT(AND).
• 'Bubbled' input indicates inversion on that input; a bubble on output indicates inversion at output.
• We want the equivalent gate symbol using input bubbles (inversions) but no output bubble.

Concept / Approach:
By De Morgan: NOT(A * B) = NOT(A) + NOT(B). Thus a NAND gate equals an OR gate whose inputs are inverted (bubbles on each input) and whose output is not inverted. That is the classic 'bubbled OR' representation.

Step-by-Step Solution:

Verification / Alternative check:
Truth-table rows for NAND and bubbled-OR match exactly: only when A=1 and B=1 is the output 0; otherwise 1.

Why Other Options Are Wrong:

• AND: would require an output bubble (that is the direct NAND symbol, not the bubbled-input equivalent).
• XAND: not a standard logic gate.
• XOR: has a different truth table.
• None of the above: incorrect because OR is correct in bubbled form.

Common Pitfalls:
Confusing bubbled input vs bubbled output, and mixing NAND with NOR equivalences (NOR ↔ bubbled AND).

Final Answer:
OR