Question

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

Answer 1

$$\begin{gathered} X=A\overline{BC}+B\overline{CA} \\ =A(\overline{B}+\overline{C})+B(\overline{C}+\overline{A}) \\ =A\overline{B}+A\overline{C}+B\overline{C}+B\overline{A} \\ =A\overline{B}+\overline{C}(A+B)+B\overline{A} \end{gathered}$$