Is there a way to represent binary operation in decimal. What I mean with this is for example a set of decimal operators that would give the same result as a x>>n a ror(x), etc. So far the only thing I reached is that $\ x>>1_{2}$ would be a $\sqrt x_{10}$ and the reverse $\ x<<1_{2}$ is $\ x^2_{10}$
EDIT:
Not sure but I would venture to say that a ROR operation would be something like $\mod(\sqrt x_{10}, 2^n)$ where n is the number of bits of the binary representation.
Shifting number $x$ right gives you $x/2$ (rounded down) and left - $2x$.
In case of ROR (I believe you meant a circular shift) you have the following: $$ x>>1 = \begin{cases} x/2 & \text{if } x_{10} = 2k \\ x/2 + 2^{N-1} & \text{if } x_{10} = 2k +1 \end{cases} $$ $$ x<<1 = \begin{cases} 2x & \text{if } x_{10} < 2^{N-1} \\ 2(x -2^{N-1}) + 1 & \text{if } x_{10} \geq 2^{N-1} \end{cases} $$
Where $n$ is a bit lenght of $x$. You may simple get $x>>n$ and $x<<n$, $\forall n \in \mathbb N$ from here.