Add a column to a table with a default value equal to the value of an existing column

How to add a column to a SQL Server table with a default value that is equal to value of an existing column?

I tried this T-SQL statement:

ALTER TABLE tablename 
ADD newcolumn type NOT NULL DEFAULT (oldcolumn) 

but it's giving an error:

The name "oldcolumn" is not permitted in this context. Valid expressions are constants, constant expressions, and (in some contexts) variables. Column names are not permitted.