Question

Design a logical circuit using AND, OR and NOT gates to evaluate  \[A \overline { BC } + B \overline{ CA }\] .

 

Answer 1

\[X = A \overline{{BC}} + B \overline{{CA}}\]
\[ = A( \overline{B} + \overline{C}) + B( \overline{C} + \bar{A})\]
\[ = A \overline{B} + A \overline{C} + B \overline{C} + B \overline{A}\]
\[ = A \overline{B} + \overline{C}(A + B) + B \overline{A}\]