$($c$)$ Below is a diagram if a single artificial neuron $($unit$)$:

The node has three inputs $x=(x1,x_2,x_3)$ that receive only binary signals $($either $0$ or $1).$ How many different input patterns can this node receive?

What if the node had four inputs? Five? Can you give a formula that computes the number of binary input patterns for a given number of inputs? $(7$ marks$)$

$($d$)$ Consider the unit shown in the Figure in question $($c$).$ Suppose that the weights corresponding to the three inputs have the following values:

and the activation of the unit is given by the step$-$function:

$(v)=\{\begin{array}{ccc}1& if& v0\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Calculate what will be the output value $y$ of the unit for each of the following input patterns: $(4$ marks$)$

$\backslash$table$[[$Pattern$,P_1,P_2,P_3,P_4$