Question:
Which of the following is a universal gate ?
Which of the following is a universal gate ?
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Just remember: "NAND and NOR can do it all." Basic gates (AND/OR/NOT) always need friends to complete a circuit.
Updated On: Aug 6, 2026
- AND
- OR
- NAND
- Inverter
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The Correct Option is C
Solution and Explanation
Concept:
• A logic gate is called "Universal" if any Boolean function can be implemented using only that type of gate.
• To be universal, a gate must be able to realize the basic boolean operations: AND, OR, and NOT.
• There are only two standard universal gates in digital logic: NAND and NOR.
Step 1: Evaluate basic gates (AND, OR, NOT/Inverter)
• An AND gate alone cannot perform inversion (NOT).
• An OR gate alone cannot perform inversion (NOT).
• An Inverter alone can only negate; it cannot combine two different inputs.
• Thus, Options (A), (B), and (D) are not universal.
Step 2: Evaluate the NAND gate
We can implement all basic gates using only NAND gates:
• NOT \(X\): Connect both inputs of a NAND gate together: \((X \cdot X)' = X'\).
• \(A\) AND \(B\): Follow a NAND gate with a NOT (made from NAND): \(((A \cdot B)')' = A \cdot B\).
• \(A\) OR \(B\): Invert inputs before a NAND gate: \((A' \cdot B')' = A + B\) (De Morgan's Law). Therefore, NAND is a universal gate.
• A logic gate is called "Universal" if any Boolean function can be implemented using only that type of gate.
• To be universal, a gate must be able to realize the basic boolean operations: AND, OR, and NOT.
• There are only two standard universal gates in digital logic: NAND and NOR.
Step 1: Evaluate basic gates (AND, OR, NOT/Inverter)
• An AND gate alone cannot perform inversion (NOT).
• An OR gate alone cannot perform inversion (NOT).
• An Inverter alone can only negate; it cannot combine two different inputs.
• Thus, Options (A), (B), and (D) are not universal.
Step 2: Evaluate the NAND gate
We can implement all basic gates using only NAND gates:
• NOT \(X\): Connect both inputs of a NAND gate together: \((X \cdot X)' = X'\).
• \(A\) AND \(B\): Follow a NAND gate with a NOT (made from NAND): \(((A \cdot B)')' = A \cdot B\).
• \(A\) OR \(B\): Invert inputs before a NAND gate: \((A' \cdot B')' = A + B\) (De Morgan's Law). Therefore, NAND is a universal gate.
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