NIMCET 2013 — Computer PYQ

1. Universal Gates

A universal gate is a gate that can implement any Boolean function without the need for any other gate type. There are two primary universal gates:

• NAND Gate

• NOR Gate

Since the NOR gate is provided in Option 2, it is the correct answer. By combining multiple NOR gates, we can create the basic logic functions: $NOT$, $AND$, and $OR$.

2. Why the other options are incorrect

• OR gate: It is a basic gate but not universal. You cannot create a $NOT$ or $NAND$ operation using only $OR$ gates.

• Exclusive OR (XOR) gates: While very useful for arithmetic, an $XOR$ gate alone cannot represent all logic functions (e.g., it cannot act as a simple $AND$ gate without additional logic).

• Multiplexers: While a Multiplexer can implement any Boolean function, it is a combinational circuit, not a single logic gate. However, in many contexts, it is considered "functionally complete," but in the context of "realizing circuits using a single gate type," the NOR gate is the standard textbook answer.

3. Realizing Basic Gates using NOR

• NOT Gate: Connect both inputs of a $NOR$ gate together: $Y=\overline{A+A}=\overline{A}$.

• OR Gate: Follow a $NOR$ gate with a $NOT$ (made from a $NOR$): $Y=\overline{\overline{A+B}}=A+B$.

• AND Gate: Use De Morgan's Law by inverting the inputs first: $Y=\overline{\overline{A}+\overline{B}}=A\cdot B$.