Question

The Boolean expression \(Y = \bar A\bar B\bar CD + \bar ABC\bar D + A\bar B\bar CD + AB\bar C\bar D\) can be minimized to

1.

\({\rm{Y}} = {\rm{\bar A\bar B\bar CD}} + {\rm{\bar AB\bar C}} + {\rm{A\bar CD}}\)

2.

\({\rm{Y}} = {\rm{\bar A\bar B\bar CD}} + {\rm{BC\bar D}} + {\rm{A\bar B\bar CD}}\)

3.

\([{\rm{Y}} = {\rm{\bar ABC\bar D}} + {\rm{\bar B\bar CD}} + {\rm{A\bar B\bar CD}}\)

4.

\({\rm{Y}} = {\rm{\bar ABC\bar D}} + {\rm{\bar B\bar CD}} + {\rm{AB\bar C\bar D}}\)

Answer 1

Correct Answer - Option 4 :

\({\rm{Y}} = {\rm{\bar ABC\bar D}} + {\rm{\bar B\bar CD}} + {\rm{AB\bar C\bar D}}\)

\(y = \overline {A} \overline {B} \overline {C} D + \bar ABC\bar D + A\overline B \overline C D + AB\overline C \bar D\)

\(\begin{array}{l} = \left( {\bar A + A} \right)\overline B \overline C D + \overline A BC\bar D + AB\bar C\overline D \\ = \overline B \overline C D + \overline A BC\bar D + AB\overline C \bar D\\ = \bar ABC\overline D + \overline B \overline C D + AB\overline C \bar D \end{array}\)