In the following digital circuit, what will be the output 'Z', when the input (A, B) are (1, 0), (0, 0), (1, 1), (0, 1):

$$\text{NAND gate output: } Y_1 = \overline{A \cdot B}$$

$$\text{OR gate output: } Y_2 = A + B$$

$$\text{AND gate output: } Y_3 = Y_1 \cdot Y_2 = (\overline{A \cdot B}) \cdot (A + B)$$

$$\text{Final NOR gate output: } Z = \overline{Y_1 + Y_3}$$

$$Z = \overline{\overline{A \cdot B} + (\overline{A \cdot B}) \cdot (A + B)} = \overline{\overline{A \cdot B}} = A \cdot B$$

$$\text{For } (A, B) = (1, 0) \implies Z = 1 \cdot 0 = 0$$

$$\text{For } (A, B) = (0, 0) \implies Z = 0 \cdot 0 = 0$$

$$\text{For } (A, B) = (1, 1) \implies Z = 1 \cdot 1 = 1$$

$$\text{For } (A, B) = (0, 1) \implies Z = 0 \cdot 1 = 0$$