Question
Design a logical circuit using AND, OR and NOT gates to evaluate $\text{A}\overline{\text{BC}}+\text{B}\overline{\text{CA}}.$
✓
Answer
$\text{X}=\text{A}\overline{\text{BC}}+\text{B}\overline{\text{CA}}$$=\text{A}\Big(\overline{\text{B}}+\overline{\text{C}}\Big)+\text{B}\Big(\overline{\text{C}}+\overline{\text{A}}\Big)$
$=\text{A}\overline{\text{B}}+\text{A}\overline{\text{C}}+\text{B}\overline{\text{C}}+\text{B}\overline{\text{A}}$
$=\text{A}\overline{\text{B}}+\overline{\text{C}}\Big(\text{A}+\text{B}\Big)+\text{B}\overline{\text{A}}$
$=\text{A}\overline{\text{B}}+\text{A}\overline{\text{C}}+\text{B}\overline{\text{C}}+\text{B}\overline{\text{A}}$
$=\text{A}\overline{\text{B}}+\overline{\text{C}}\Big(\text{A}+\text{B}\Big)+\text{B}\overline{\text{A}}$
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