DRDO CSE 2022 Paper 1 | Question: 25

Question

Simplify the Boolean function $F=W^{\prime} X^{\prime} Y^{\prime}+W X^{\prime} Y^{\prime}+W^{\prime} X Y Z^{\prime}+X^{\prime} Y Z^{\prime}$

Answer 1

$F= \bar w\bar x\bar y+w\bar x\bar y+\bar wxy\bar z+\bar xy\bar z$

$\implies F= \bar w\bar x\bar y(z+\bar z)+w\bar x\bar y(z+\bar z)+\bar wxy\bar z+(w+\bar w)\bar xy\bar z$

$\implies F=\bar w\bar x\bar yz+\bar w\bar x\bar y\bar z+w\bar x\bar yz+w\bar x\bar y\bar z+\bar wxy\bar z+w\bar xy\bar z+w\bar xy\bar z $

$\implies F=\sum (0,1,2,6,8,9,10)$

 solve using k-map we get

$F=\bar x\bar y+w\bar xz+\bar w y\bar z $