The checksum digit algorithm for a 12-digit BarCode goes like this:

Assume the a BarCode number looks like this D1D2D3D4........D12 where Di are digits 0 to 9

sum up all the odd digits to a sum of S1
sum up all the even digit to a sum of S2
subtract S2 from S1 , do the modulu from 10 and then give the absolute positive value

The value of abs ((S1-S2)mod 10) IS the BarCode checksum digit.

Here is the suggested function code for the T-SQL BARCODE checkSum function:

Create  function dbo.fn_BarCode_checkSum (@cBarcode char(12))
-- By Eli Leiba
-- 08/2005
returns  Int
as 
 begin 

  declare @barCodeCheckRes Int
  declare @idx     tinyInt
  declare @sgn     Int
  
  set   @barCodeCheckRes = 0
 
  -- check if given Barcode is Numeric , if not return error status -1  
  if (IsNumeric (@cBarcode) = 0) return -1

  -- check if BarCode length of number is 12 , if not return error status -2
  if (Len (rtrim(ltrim(@cBarcode))) != 12)  return -2

  -- start the compute BarCode checksum algorithm
  
  set @idx = 1
  while (@idx <= 12)
  begin 
     -- Calculate sign of digit (- for even digit and + for an odd digit 
     if ((@idx % 2) = 0) 
 set @sgn = -1
     else 
        set @sgn = +1

     set  @barCodeCheckRes = @barCodeCheckRes +
             convert (tinyInt, substring (@cBarcode,@idx,1)) * @sgn
     set @idx = @idx + 1    
  end 

  -- return the resulting digit,
  return ( abs(@barCodeCheckRes % 10))
end 
go

Here is an Example for the function execution for two 12 Length Barcodes:

select dbo.fn_BarCode_checkSum  ('283723281122') as FirstBarc,
 dbo.fn_BarCode_checkSum ('123253245433') as SecondBarc

FirstBarc SecondBarc
7 1

Lets check :

dbo.fn_BarCode_checkSum ('283723281122') = | (2 - 8 + 3 - 7 + 2 - 3 + 2 - 8 + 1 - 1 + 2 - 2)%10|
= | ( -6 -4 -1 -6 + 0 + 0)%10| = |-17 % 10| = |-7| = 7

dbo.fn_BarCode_checkSum ('123253245433') = | (1 - 2 + 3 - 2 + 5 - 3 + 2 - 4 + 5 - 4 + 3 - 3)%10| =
| (-1 + 1 + 2 - 2 + 1 + 0) %10| = |(0 + 0 + 1 + 0)%10| = |1| = 1

Remarks