Convert a Non-Linear Constraint of Integer and continuous variables to a Linear Constraint for programming

I'm going to drop the subscripts and superscripts for $NN$ and $w$ and just show how to handle one product $w\cdot NN$. I'm also going to assume that both $NN$ and $w$ have known upper bounds.

Step 1 is to introduce binary variables $x_i$ and $y_j$, along with the constraints $$w=\sum_{i=0}^I 2^i x_i$$ and $$NN=\sum_{j=0}^J 2^j y_j.$$The values of $I$ and $J$ depend on the bounds for $w$ and $NN$. Also introduce a variable $s \ge 0$ to represent the product: $s = w\cdot NN$. ($s$ will be integer-valued, but you can declare it as a continuous variable.)

Next, for each pair $(i,j)\in \{0,\dots,I\}\times \{0,\dots,J\}$, introduce a continuous variable $z_{ij}\in [0,1]$ along with the constraints $$z_{ij} \le x_i$$ $$z_{ij}\le y_j$$and $$z_{ij}\ge x_i + y_j - 1.$$These enforce $z_{ij} = x_i y_j$. Finally, add the following:$$s = \sum_{i=0}^I\sum_{j=0}^J 2^{i+j}z_{ij}.$$