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Consider this string:
1 1 1
When I mark the first two 1s in visual mode and then :'<,'>s/1/2/g, all 1s on the line are replaced by 2s, not just those in the selected region. Why is this the case and how can I restrict the operation to the selected text?
The :s[ubstitue] command operates on whole lines and the [range] prefix is a range of lines.
To restrict the operation to just the visually-selected region, you can use the \%V atom in your search pattern. That is, visually-select the first two 1s in your example, then use this command to replace just those 1s:
'<,'>s/\%V1/2/g
See also
:help /\%V
The :help entry says to put \%V at the start and end of the pattern, but I didn't read that before trying it and it worked in the example here with \%V at just the start of the pattern.
That is, because you have provided only a line-based range for the :s command. There is no way to have an ex command apply to only a column-based selection. Specifically for the :s command there exists the \%V regex atom, that allows to substitute within a selection only.
