Minimum number of 2-input NAND gates required to implement the Boolean function given below is _______.

$f = (¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B) (C + D)$
4

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Solution

The correct option is A 4
$f = (¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B) (C + D)$

$= ¯ ¯¯¯¯¯¯ ¯ A B (C + D) = ¯ ¯¯¯¯¯¯ ¯ A B . C + ¯ ¯¯¯¯¯¯ ¯ A B D$

$= ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ ¯ ¯¯¯¯¯¯ ¯ A B C + ¯ ¯¯¯¯¯¯ ¯ A B D$

$= ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ ¯ ¯¯¯¯¯¯ ¯ A B C . ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ ¯ ¯¯¯¯¯¯ ¯ A B D$

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