By taking an AND gate and adding an inverter at each input and at the output, what overall logic function is realized?

Introduction / Context:
Gate transformations using input and output inversions are classic applications of De Morgan's laws. Recognizing these equivalences helps minimize hardware, convert between families, and understand logic simplification. This question asks for the composite function when an AND gate is surrounded by inverters on all inputs and on the output.

Given Data / Assumptions:

• Start with a multi-input AND gate.
• Invert every input and invert the output.
• Assume positive logic and ideal inversions.

Concept / Approach:

Let the inputs be A and B for illustration. The inner gate computes AND of the inverted inputs: AND(NOT A, NOT B). The outer inversion then negates the result: NOT(AND(NOT A, NOT B)). By De Morgan's law, NOT(X AND Y) = (NOT X) OR (NOT Y). Substituting X = NOT A and Y = NOT B yields A OR B. This generalizes to more than two inputs as well.

Step-by-Step Solution:

Verification / Alternative check:

Truth table evaluation confirms that the final output equals 1 whenever either A or B equals 1, matching the OR function.

Why Other Options Are Wrong:

NAND arises from inverting only the output of AND. NOR arises from inverting only the output of OR. XOR is unrelated to complete inversion of inputs and output around AND.

Common Pitfalls:

Forgetting which side is inverted or applying De Morgan incorrectly. Another mistake is assuming that inverting both inputs to AND yields OR directly without the final output inversion.

Final Answer:

OR