$($a$)$ To simulate the perceptron algorithm for a two$-$input XNOR gate with a learning rate of $0\mathrm{.}02$ and a threshold of $0\mathrm{.}2,$ you would need to define the initial weights and bias, then iteratively update them based on the perceptron learning rule until the output matches the desired output $(0$ or $1)$ for all possible input combinations.