........... is an Universal gate.

Question

Accepted Answer

The correct option is (2):
A universal gate is a logic gate that, by itself, can be used to construct any other logic gate (AND, OR, NOT, XOR, NOR, etc.). The NAND gate, an abbreviation for NOT-AND, is one of the two standard universal gates in digital electronics, the other being the NOR gate. Its functional completeness is a highly valuable property in practical circuit design. This means that a circuit designer can use just one type of physical integrated circuit (IC) containing NAND gates to build a system of any complexity, which greatly simplifies inventory, manufacturing, and reduces overall cost. For example, by connecting a single NAND gate's inputs together, it functions as a NOT gate; two NAND gates can form an AND gate; and three NAND gates can form an OR gate, proving its universality.

The incorrect option is (1):
The AND gate is a fundamental logic gate, not a universal gate. It performs the logical multiplication of its inputs, only yielding a high (1) output when all inputs are simultaneously high. The core reason it fails to be a universal gate is its inability to perform the NOT (inversion) operation using only itself. The NOT function is essential for functional completeness, as it is required to transform basic operations into their complements, or to realize other complex gates. Therefore, while crucial, the AND gate must be combined with a NOT gate (or its equivalent) to become functionally complete.

The incorrect option is (3):
The XOR (Exclusive-OR) gate is a derived gate that outputs high only when an odd number of its inputs are high, effectively performing an inequality check. It is not a universal gate because it is functionally incomplete. Specifically, an XOR gate cannot be configured solely to perform the NOT function, which is a necessary building block for all other logic gates. Furthermore, using only XOR gates, it is impossible to generate the AND or OR functions required for general Boolean expression implementation.

The incorrect option is (4):
The XNOR (Exclusive-NOR) gate is another derived gate that acts as an equivalence checker, outputting high only when all its inputs are the same. Like its complement, the XOR gate, the XNOR gate is not a universal gate. This is because a set of XNOR gates cannot, by itself, implement the fundamental NOT operation, which is a prerequisite for a gate to be considered universal. Since it cannot realize a NOT gate and subsequently other basic gates like AND or OR, the XNOR gate lacks the complete set of logical functions needed to build any arbitrary digital circuit.