Credit Card Number Check. The last digit of a credit card numberis the check digit, which protects against transcription errorssuch as an error in a single digit or switching two digits. Thefollowing method is used to verify actual credit card numbers but,for simplicity, we will describe it for numbers with 8 digitsinstead of 16:
• Starting from the rightmost digit, form the sum of every otherdigit. For example, if the credit card number is 4358 9795, thenyou form the sum 5 + 7 + 8 + 3 = 23.
• Double each of the digits that were not included in thepreceding step. Add all digits of the resulting numbers. Forexample, with the number given above, doubling the digits, startingwith the next-to-last one, yields 18 18 10 8. Adding all digits inthese values yields 1 + 8 + 1 + 8 + 1 + 0 + 8 = 27.
• Add the sums of the two preceding steps. If the last digit ofthe result is 0, the number is valid. In our case, 23 + 27 = 50, sothe number is valid. Write a program in Java that implements thisalgorithm. The user should supply an 8-digit number, and you shouldprint out whether the number is valid or not. If it is not valid,you should print the value of the check digit that would make itvalid.
