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NAND as a Universal Gate — Using only NAND gates, which standard logic function(s) can be implemented without needing any other gate type?

Difficulty: Easy

Correct Answer: Any of the above

Explanation:


Introduction:
The NAND gate is called a universal gate because, by appropriate interconnection, it can realize every basic logic function. This question checks whether you know that NAND alone can synthesize NOT, AND, and OR, and therefore any combinational logic circuit.

Given Data / Assumptions:

  • Only 2-input NAND gates are available.
  • Binary logic levels are ideal (0 and 1).
  • No constraints on the number of stages, other than logical feasibility.


Concept / Approach:
A universal gate set can implement all other gates. With NAND: NOT is obtained by tying a gate’s inputs together; AND is obtained by NAND followed by NOT; OR is obtained via De Morgan by inverting inputs into a NAND (i.e., OR = NOT(A) NAND NOT(B)).

Step-by-Step Solution:

1) Inverter: NOT A = A NAND A.2) AND: A AND B = NOT(A NAND B) = (A NAND B) NAND (A NAND B).3) OR: A OR B = NOT(NOT A AND NOT B) = (A NAND A) NAND (B NAND B).


Verification / Alternative check:

Build truth tables or simulate the three constructions; each matches the target gate across all input pairs.


Why Other Options Are Wrong:

OR gate: True that NAND can make OR, but the option claims only OR. NAND can do more.AND gate: Same issue—NAND can make AND but is not limited to it.Inverter (NOT): Also derivable, but not the only possibility.


Common Pitfalls:

Forgetting the NOT-with-tied-inputs trick (A NAND A).Missing De Morgan’s law when deriving OR from NAND.


Final Answer:

Any of the above
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