Question

If the complements of inputs are available, minimum number of 2 input NAND gates required to realize the mentioned below function will be _______

$F(A,B,C,D)=B\overline{D}+\overline{B}CD+ABC+AB\overline{C}D+\overline{B}\overline{D}$

• A. 5

Answer 1

The correct option is A 5

From K- Map,
$F=\overline{D}+\overline{B}C+AB$

Alternatively
$F=B\overline{D}+\overline{B}CD+SBC+AB\overline{C}D+\overline{B}\overline{D}$
$=\overline{D}(B+\overline{B})+\overline{B}CD+ABC+AB\overline{C}D$
$=\overline{D}+\overline{B}CD+ABC+ABC+AB\overline{C}D$
$=\overline{D}+\overline{B}CD+AB(C+\overline{C}D)$
$=\overline{D}+\overline{B}CD+AB\left[\right(C+\overline{C}\left)\right(C+D\left)\right]$
$=\overline{D}+(\overline{B}C+AB)D+ABC$
$=(\overline{D}+D)(\overline{D}+\overline{B}C+AB)+ABC$
$F=\overline{D}+\overline{B}C+AB$
Now realization



Hence required number of NAND gates = 5