In this problem, you will implement a recurrent neural network which

implements binary addition. The inputs are given as binary sequences, starting with

the least significant binary digit. The sequences will be padded with at least one zero

on the end. For instance, the problem

$100111+110010=1011001$

would be represented as:

$$ Input $1$: $1,1,1,0,0,1,0$

$$ Input $2$: $0,1,0,0,1,1,0$

$$ Result: $1,0,0,1,1,0,1$

Design the weights and biases for an RNN which has two input units, three hidden

units, and one output unit, which implements binary addition. All of the units use the

hard threshold activation function $($f$($x$)=1$ if x $>0$ and $0$ otherwise$).$ In particular,

specify weight matrices U$,$ V $,$ and W$,$ bias vector bh$,$ and scalar bias by for the following

architecture:

Hint: In the addition algorithm, you add up the values in each column, including the

carry. Have one of your hidden units activate if the sum is at least $1,$ the second one if

it is at least $2,$ and the third one if it is