Question

Which of the following logic gates is a universal gate?

• A. AND
• B. OR
• C. NOT
• D. NAND

Hint:

The two universal logic gates are NAND and NOR. This is a fundamental concept in digital electronics and a common exam question. Remember that any Boolean expression can be implemented using only NAND gates or only NOR gates.

Answer 1

The Correct Option is D

A universal logic gate is a gate that can be used to implement any other type of logic gate (like AND, OR, NOT, XOR, etc.).
There are two universal gates: NAND and NOR.
Let's see how a NAND gate can be used to create the three basic gates:
1. NOT Gate from NAND: If both inputs of a NAND gate are connected together (A), the output is $\overline{A \cdot A} = \overline{A}$, which is the function of a NOT gate.
2. AND Gate from NAND: An AND gate is a NAND gate followed by a NOT gate. Since we can make a NOT gate from a NAND gate, we can create an AND gate by connecting the output of one NAND gate to both inputs of a second NAND gate. Output = $\overline{\overline{A \cdot B}} = A \cdot B$.
3. OR Gate from NAND: Using De Morgan's laws, $A+B = \overline{\overline{A+B}} = \overline{\overline{A} \cdot \overline{B}}$. This means we need to NOT the inputs first and then NAND them. This can be done using three NAND gates.
Since all basic logic functions can be constructed from NAND gates alone, the NAND gate is a universal gate.
The same is true for the NOR gate. AND, OR, and NOT are basic gates but are not universal.