Representational Power of Perceptrons

Decision surface of two-input ( $x_{1}$ and $x_{2}$ ) perceptron.

We can view the perceptron as representing a hyperplane decision surface in n-dimensional space of instances.
Test: Which weights represent $g (x_{1}, x_{2}) = AND (x_{1}, x_{2})$ ? $w_{0} = - . 8, w_{1} = w_{2} = . 5$ which is the line $y = \frac{8}{5} - x$ .
Notice that example (b) is not linearly separable. It is an XOR.
Perceptrons cannot represent XOR, so we will need networks of them.