Considering the bitwise OR operation, wikipedia states,
$$x\;\mathrm{OR}\;y = \sum_{n=0}^b 2^n\left[\left[\left(\lfloor\frac{x}{2^n}\rfloor\mod2\right)+\left(\lfloor\frac{y}{2^n}\rfloor\mod2\right)\\+\left(\lfloor\frac{x}{2^n}\rfloor\mod2\right)\left(\lfloor\frac{y}{2^n}\rfloor\mod2\right)\mod 2\right]\mod2\right]$$
where $b$ is the number of bits in $x = \lfloor\log_2x\rfloor+1$ for all $x\neq0$
I can see that $\left(\lfloor\frac{x}{2^n}\rfloor\mod2\right)$ and $\left(\lfloor\frac{y}{2^n}\rfloor\mod2\right)$ are the $n^{th}$ bits of x and y, respectively, but I'm having a hard time putting the rest of the derivation together.
