Question

Consider a Boolean expression
$f=(B+BC)(B+\overline{B}C)(B+D)$

The minimum number of NAND-gates required to implement this function ${}^{\prime }{f}^{\prime }$ will be __________

Answer 1

Given, $f=(B+BC)(B+\overline{B}C)(B+D)$

$=(BB+BCB+B\overline{B}C+BC\overline{B}C)(B+D)$

$=BB+BD=B+BD=B(1+D)$

$f=B$
So, it is clear that output ${}^{\prime }{f}^{\prime }$ can be directly obtained from input ${}^{\prime }{B}^{\prime }$. So, the number of NAND-gates required is zero.