I was wondering what would be a time complexity of shifting a binary or a decimal number? For example: 0011, when I shift it left I get 0001.
I was thinking that the time complexity is $\Theta(n)$, because we have to shift every number.
I need it to calculate $m*{b^\frac{n}{2}}$, where $m$ is some number and $b$ might be 2 (in case of binary) or 10 (decimal). Therefore instead of multiplication, I just shift to multiply, and therefore complexity is $\Theta(n)$.
Am I correct or is my thinking wrong?