qgis - Use field calculator to change values from a,b,c etc. to 1,2,3 etc.?

I have a vector shapefile with a column with string values. How can I convert this to a column of integer values in another column but keep the categorization.

e.g. from:

col1,newcol2
A,
A,
B,
A,
C,

to:

col1,newcol2
A,1
A,1
B,2
A,1
C,3

I'm sure it is in the 'replace' or 'case when' syntax somewhere but I cannot find a clear method via Google etc.