Step 1: Understanding the Concept:
We must analyze the combinatorial logic gates to derive the boolean expression for the output.
Then evaluate it for specific boolean inputs. Step 2: Key Formula or Approach:
Identify the logic operations:
NOT gate gives $\bar{A}$.
NAND gate gives $\overline{B \cdot C}$.
OR gate gives the sum of its inputs.
Final Boolean Expression: $Y = \bar{A} + \overline{B \cdot C}$. Step 3: Detailed Explanation: Condition 1: All inputs are low (0).
$A = 0, B = 0, C = 0$.
Substitute into expression:
\[ Y = \bar{0} + \overline{0 \cdot 0} \]
\[ Y = 1 + \bar{0} \]
\[ Y = 1 + 1 \]
According to Boolean OR logic, $1 + 1 = 1$.
So, output is $1$ (High). Condition 2: All inputs are high (1).
$A = 1, B = 1, C = 1$.
Substitute into expression:
\[ Y = \bar{1} + \overline{1 \cdot 1} \]
\[ Y = 0 + \bar{1} \]
\[ Y = 0 + 0 \]
According to Boolean OR logic, $0 + 0 = 0$.
So, output is $0$ (Low).
The outputs are respectively $1$ and $0$. Step 4: Final Answer:
The outputs are (1, 0).
