How to merge multiple columns

I'm currently working on building a database in SQL Server 2008R2 to hold UPC-A codes. The UPC codes are currently split into three different columns, the first one has the first six digits followed the second column holding the next five digits and the third holding the check digit. I want to add another column that holds all 12 digits of the UPC code.

Is there a way to merge all three segmented pieces of the UPC code into a single column and if so is there a way to get the column to populate when a new UPC code is added to the database?

Thanks