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Question $3$: Learning a Boolean logic gate

Construct a perceptron that computes the output of a NOR gate, whose truth table is given below $($where $0$ represents False and $1$ represents True$).$ Use a learning rate of $\backslash$alpha $=0\mathrm{.}5$

$,$ a bias term x$0=1$

$,$ and the initial weight vector w$=($w$0,$w$1,$w$2)$T$=(0,0,0\mathrm{.}5)$T

$.$ What are the final values of the weight vector after applying the perceptron learning algorithm? Assume that data is iterated over from top to bottom.

X$1$ X$2$ NOR

$001$

$010$

$100$

$110$

Please enter the values of the weight vector into the appropriate boxes.

w$=($w$0,$w$1,$w$2)$T$=($

Answer $1$ Question $3$

$0$

$,$ Answer $2$ Question $3$

$0$

$,$ Answer $3$ Question $3$

$-0\mathrm{.}5$

$)$T

Activation function:

g$($z$)=1$

if z$>1$

and g$($z$)=0$

otherwise.