GATE EE 1999 Digital Electronics Q 1 - Grad Plus
GATE EE 1999 Digital Electronics Q 1

GATE EE 1999 Digital Electronics Q 1

The logic function f=\overline{\left(x.y\right)+(\overline x.y)} is the same as

a) f=\left(x+y\right)\left(\overline x+\overline y\right)

b) f=\overline{\left(\overline x+\overline y\right)\;\left(x+y\right)}

c) f=\overline{\left(x.y\right)}\;\left(\overline x.\overline y\right)

d) none of the above

Ans: (b)

Explanation

f=\overline{\left(x\cdot\overline y\right)+\left(\overline x\cdot y\right)}=\overline{\left(x\cdot\overline y\right)}\cdot\overline{\left(\overline x\cdot y\right)} =\left(\overline x+y\right)\cdot\left(x+\overline y\right)=xy+\overline x\;\overline y

Simplifying option (b) we have,

\overline{\left(\overline x+\overline y\right)\;\left(x+y\right)}=\left(\overline{\overline x+\overline y}\right)+\left(\overline{x+y}\right) =xy+\overline x\;\overline y\;=f
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