etermine if the credit card nu 9173 is VALID or NOT?

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter86: Bcd (binary Coded Decimal) Numeration Systems
Section: Chapter Questions
Problem 46A
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Question
a) Determine if the credit card number: 4578 4562
5643 9173 is VALID or NOT?
Transcribed Image Text:a) Determine if the credit card number: 4578 4562 5643 9173 is VALID or NOT?
Application 5: Credit Cards
Like ISBN and UPC codes, credit card numbers can be easily checked by the "check digit". In the
Philippines, Visa and Master cards are the dominant credit cards in the market, normally 16-digit except
for some Visa cards that have 13 digits only.
Credit cards numbers can be checked by doubling every other digit starting from the second (when
counted from the right) to the last digit (the last digit being check digit), and summing up all resulting
numbers. If the doubled digit results in a 2-digit number, simply treat the two digits as separate digits. The
card number is valid only if the sum of the digits under modulo 10 is congruent to 0.
Example
Determine which credit card number is valid and which is not valid.
a) 5234 8213 3410 1298
b) 6011 0123 9145 2317
Solutions
a)
Digits
52 3
8 2
13
4 10 1 2 9 8
4
Doubled
(alternate)
10 2
16 2
6 4 2 0 2 2 18 8
3
Sum = 1+0+2 + 6 + 4 +1+6+ 2 +2 +3+ 6+ 4 + 2 +0+2 + 2 +1+8+8 = 60 mod 10 = 0,
the indicated credit card number is VALID.
b)
Digits 6 0 1
101
2 391 4 5 2 3 17
Doubled
12 0 2 1 01 4 3
18 18 5 4 3 2 7
(alternate)
Sum = 1+ 2+0 + 2 +1+0 + 4 + 3 +1+8 +1+ 8+5 +4 +3 + 2 +7
= 53 mod 10 = 3, the indicated credit card number is INVALID.
2.
4.
6
Transcribed Image Text:Application 5: Credit Cards Like ISBN and UPC codes, credit card numbers can be easily checked by the "check digit". In the Philippines, Visa and Master cards are the dominant credit cards in the market, normally 16-digit except for some Visa cards that have 13 digits only. Credit cards numbers can be checked by doubling every other digit starting from the second (when counted from the right) to the last digit (the last digit being check digit), and summing up all resulting numbers. If the doubled digit results in a 2-digit number, simply treat the two digits as separate digits. The card number is valid only if the sum of the digits under modulo 10 is congruent to 0. Example Determine which credit card number is valid and which is not valid. a) 5234 8213 3410 1298 b) 6011 0123 9145 2317 Solutions a) Digits 52 3 8 2 13 4 10 1 2 9 8 4 Doubled (alternate) 10 2 16 2 6 4 2 0 2 2 18 8 3 Sum = 1+0+2 + 6 + 4 +1+6+ 2 +2 +3+ 6+ 4 + 2 +0+2 + 2 +1+8+8 = 60 mod 10 = 0, the indicated credit card number is VALID. b) Digits 6 0 1 101 2 391 4 5 2 3 17 Doubled 12 0 2 1 01 4 3 18 18 5 4 3 2 7 (alternate) Sum = 1+ 2+0 + 2 +1+0 + 4 + 3 +1+8 +1+ 8+5 +4 +3 + 2 +7 = 53 mod 10 = 3, the indicated credit card number is INVALID. 2. 4. 6
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