Topic: Digital Circuits
For a logic circuit with inputs A, B, and C, if the output is $Z = Y_3 + Y_2$ where intermediate signals are $Y_3 = A \cdot B \cdot (\overline{A \cdot \overline{C}})$ and $Y_2 = A \cdot B \cdot C$, the simplified expression for Z is
- A. $\overline{A\overline{C}}AB$
- B. $ABC$
- C. $ABC + ACB$
- D. $ABC + CB$
Answer: B. $ABC$
Explanation: We can simplify the boolean expression step by step. First, simplify $Y_3$: $Y_3 = AB(\overline{A\overline{C}})$. Applying De Morgan's law: $Y_3 = AB(\overline{A} + C) = AB\overline{A} + ABC$. Since $A\overline{A} = 0$, $Y_3 = ABC$. We are given $Y_2 = ABC$. The final output is $Z = Y_3 + Y_2 = ABC + ABC = ABC$.