Let p$\_$n$=$parity$($x$\_1,$x$\_2,...,$x$\_$n$).$

Show a neural network that calculates p$\_5.$

Show a neural network that calculates p$\_63.$

Show a neural network that calculates p$\_256.$

Write down the gradient descent update equations for a network to calculate p$\_8.$

Train such a neural network and show weights and the output for each of

$01110101,$

$11011010,$

$10101001,$

$11111111,$