Question

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

1. f = (x + y)(x̅ + y̅)
2. \(f = \overline {\left( {\bar x + \bar y} \right)\left( {x + y} \right)} \)
3. \(f = \overline {\left( {x.y} \right)} \left( {\bar x.\bar y} \right)\)
4. None of the above

Answer 1

Correct Answer - Option 2 : \(f = \overline {\left( {\bar x + \bar y} \right)\left( {x + y} \right)} \)

Analysis:

\(f = \overline {x \cdot \bar y + \bar x \cdot y} \)

\( = \overline {x \oplus y} \)

= x ⊙ y

Looking through the options,

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

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

= x ⊙ y