When analyzing logic circuits, identify the gates and work from the input terminals forward to the output terminal, documenting the truth table values at each node.
Step 1: Recall the NAND rule. A NAND gate gives output $0$ only when both its inputs are $1$. In every other case it gives $1$. Keep that single rule handy as we trace the circuit. Step 2: Note the fixed input levels. The circuit feeds in a constant $A = 1$ and a constant $B = 0$, and the $0$ first passes through a NOT gate (inverter). Step 3: Invert the 0. The NOT gate turns the $0$ into a $1$, so this branch now carries a logic $1$ onward to the next gates. Step 4: Evaluate the first NAND stage. Following the static logic levels through the lower NAND gate with its incoming signals, that gate settles to an output of $0$. Step 5: Evaluate the gate that produces Y. The gate giving $Y$ receives at least one $0$ from the previous stage. Since a NAND with a $0$ input must output $1$, the output stabilises at $Y = 1$. Step 6: Conclude. The feedback settles to a steady state with $Y = 1$, matching option 2. \[ \boxed{1} \]
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