Final answer:
To make a UPC valid, follow the specific format and perform a check digit calculation. The check digit can be calculated using a formula. For the UPC 1-214867-5309-d, the check digit is 10 - (10 + d) % 10.
Step-by-step explanation:
To make a UPC (Universal Product Code) valid, you need to follow a specific format and perform a check digit calculation. The UPC consists of three parts: the Manufacturer Number, the Product Number, and the Check Digit. The Manufacturer Number is typically 6 digits, the Product Number is usually 5 digits, and the Check Digit is the last digit of the UPC.
- Separate the UPC into its individual digits.
- Sum the digits at the odd positions (1st, 3rd, 5th, etc.) and multiply the result by 3.
- Sum the digits at the even positions (2nd, 4th, 6th, etc.).
- Add the results from steps 2 and 3.
- Find the smallest number that, when added to the result from step 4, creates a multiple of 10.
- The check digit is the difference between the number found in step 5 and the result from step 4.
For example, let's take the UPC 1-214867-5309-d. By following the steps above, we can calculate the check digit as follows:
- 1 + 8 + 7 + 3 + 0 + d = 19 + d
- (2 + 4 + 6 + 5 + 0) * 3 = 51
- 19 + d + 51 = 70 + d
- 70 + d + x = 10n (where x is the check digit and n is a whole number)
- If we subtract 70 from 10n, we get x + d = 10n - 70
- The smallest value of x that satisfies this equation is 10 - (10 + d) % 10
Therefore, the check digit for the UPC 1-214867-5309-d is: 10 - (10 + d) % 10.