What is De Morgan’s theorem used for in digital logic?

Correct Answer (Detailed Explanation is Below)

D. More than one of the above

Detailed Explanation

De Morgan’s Theorem in digital logic states:

• The complement of a sum equals the product of the complements

• The complement of a product equals the sum of the complements

For example:

$$(A + B)' = A'B'$$$$(AB)' = A' + B'$$

Uses in Digital Logic

1️⃣ Simplifying Boolean expressions
It helps convert expressions into simpler forms during logic circuit design.

2️⃣ Implementing NAND/NOR gate circuits
Using De Morgan’s theorem, AND–OR circuits can be converted to NAND or NOR implementations, which are widely used in hardware.

3️⃣ Not used for binary addition
Binary addition is performed by half adders and full adders, not by De Morgan’s theorem.

Checking Options

• (A) Simplifying Boolean expressions ✔

• (B) Implementing NAND gates ✔

• (C) Performing binary addition ✖

Since A and B are correct, the answer is:

✅ (D) More than one of the above.