I'm writing an academic paper and encountered the problem that what notations should I use for bit-wise Boolean addition, e.g.
$$\begin{array}{r} 0101 \\ +\ 0011 \\ \hline 0111 \end{array}$$
because for every bit $1+0=0+1=1+1=1$, and $0+0=0$.
If I use "$+$" it may be misunderstood as normal integer addition. But the notation "or" $\vee$ is used for one bit operation, e.g. $0\vee 1=1$.
So what noations should I use ?
You may overload the $\vee$ operator for "bitwise or".
$0001\vee 0100 = 0101$