1. The problem is to implement the Boolean expression $$y = AC + BC\overline{} + ABC\overline{}$$ as a logic circuit. 2. First, identify the variables and their complements: inputs are $$A$$, $$B$$, and $$C$$; $$\overline{B}$$ is the NOT of $$B$$. 3. Break down the expression into parts: - $$AC$$: AND gate with inputs $$A$$ and $$C$$. - $$BC\overline{}$$: AND gate with inputs $$\overline{B}$$ (NOT of $$B$$) and $$C$$. - $$ABC\overline{}$$: AND gate with inputs $$A$$, $$B$$, and $$\overline{C}$$ (NOT of $$C$$). 4. To get $$\overline{B}$$ and $$\overline{C}$$, use NOT gates on $$B$$ and $$C$$ respectively. 5. The outputs of these three AND gates are then combined using an OR gate to produce the final output $$y$$. 6. The circuit structure: - Input $$A$$ splits to two AND gates: one with $$C$$ for $$AC$$, and one with $$B$$ and $$\overline{C}$$ for $$ABC\overline{}$$. - Input $$B$$ goes through a NOT gate to get $$\overline{B}$$, which then goes to an AND gate with $$C$$ for $$BC\overline{}$$. - The outputs of the three AND gates feed into an OR gate to produce $$y$$. Final Boolean expression implemented: $$y = AC + B\overline{C} + AB\overline{C}$$.