Question

Which of the following logic gates are called universal gates?

• A. NOT and AND
• B. AND and OR
• C. Ex-OR and Ex-NOR
• D. NAND and NOR

Hint:

In many integrated circuit (IC) manufacturing processes, it is actually easier and cheaper to manufacture many NAND gates than it is to mix different gate types. This is why NAND-NAND logic is very common in hardware design.

Answer 1

The Correct Option is D

1. The Two Universal Gates: There are only two basic logic gates that are considered universal:

• NAND Gate: (NOT AND)

• NOR Gate: (NOT OR)

2. Proof by Implementation: To be universal, you must be able to create a NOT, AND, and OR gate from them:

• NOT from NAND: Connect both inputs of a NAND together.

• AND from NAND: Follow a NAND gate with a NAND-configured NOT.

• OR from NAND: Use De Morgan's Law; invert the inputs using NAND-NOTs and feed them into another NAND.

3. Why the others are not universal:

• AND and OR: These are called "basic gates," but you cannot create a NOT (inversion) using only AND or OR gates.

• NOT: You cannot create multi-input logic like AND or OR using only NOT gates.
Because NAND and NOR can reconstruct the entire set of Boolean operations, they are the only universal gates in the provided list.