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Question 88

Computer Awareness Boolean algebra Easy

Consider the circuit shown below and find minimum number of NAND gates required to design it.

Question Image
(A) 4
(B) 6
(C) 3
(D) 5
โœ“ Correct Answer: Option A Verified Solution

๐Ÿ“˜ Step-by-Step Solution & Detailed Explanation:

The circuit in the figure is a single 2-input NOR gate: \(Y = \overline{A + B}\).

Building it with NAND gates only:

  1. NAND 1: \(\overline{A \cdot A} = \bar{A}\)
  2. NAND 2: \(\overline{B \cdot B} = \bar{B}\)
  3. NAND 3: \(\overline{\bar{A} \cdot \bar{B}} = A + B\) (De Morgan's law)
  4. NAND 4: invert it to get \(\overline{A + B}\)

Minimum = 4 NAND gates.

Answer: (A) 4

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