function ean13_check_digit($digits) {
      //first change digits to a string so that we can access individual numbers
      $digits =(string)$digits;
      // 1. Add the values of the digits in the even-numbered positions: 2, 4, 6, etc.
      $even_sum = $digits{1} + $digits{3} + $digits{5} + $digits{7} + $digits{9} + $digits{11};
      // 2. Multiply this result by 3.
      $even_sum_three = $even_sum * 3;
      // 3. Add the values of the digits in the odd-numbered positions: 1, 3, 5, etc.
      $odd_sum = $digits{0} + $digits{2} + $digits{4} + $digits{6} + $digits{8} + $digits{10};
      // 4. Sum the results of steps 2 and 3.
      $total_sum = $even_sum_three + $odd_sum;
      // 5. The check character is the smallest number which, when added to the result in step 4,  produces a multiple of 10.
      $next_ten = (ceil($total_sum/10))*10;
      $check_digit = $next_ten - $total_sum;
      return $digits . $check_digit;
      }