For the circuit shown above, the equivalent gate is:
Looking at the circuit: - The circuit consists of two gates: an AND gate and a NOT gate (in the form of an inverter).
- The inputs \( A \) and \( B \) are first passed through the AND gate.
- The output of the AND gate is then passed through a NOT gate (inverter). This combination of an AND gate followed by a NOT gate is equivalent to a NAND gate, as the NAND gate is the negation of the AND gate. Thus, the equivalent gate is a NAND gate.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: