How to convert a mod 2 function to an expression in Boolean Algebra

Question

I'm not sure if this is the right place to post it but I have a question I'm having a hard time understanding. The questions is:

Convert the function $X^3Y + 2XZ + WX + W$ mod $2$ to an expression in Boolean algebra.

My professor told us that the answer is:

The mod 2 expression $X^3Y + 2XZ + WX + W$ is equivalent in mod 2 to $XY+W(X+1)$ so this mod 2 expression is $XY x$ or $WX'$ in boolean algebra or $XY(WX')' + WX(XY)'$.

I don't understand how he got $XY + W(X+1)$ out of.

Thanks in advance.

Answer 1

$X^3$ is always congruent with $X$ mod 2, so $X^{3}Y$ can be replaced with $XY$. $2XZ$ is always congruent with 0, so you can leave it out. Finally, $WX+W$ can be factored as $W(1+X)$, and since $X'=1+X$, you get $WX'$. Summing all results, you get $XY+WX'$ as your professor said.