INTERNATIONAL STANDARD BOOK NUMBER (ISBN)
Formula:
ISBN- 13 digit code
X13 = 10 – (X1 + 3X2 + X3 + 3X4 + X5 + 3X6 + X7 + 3X8 + X9 +
3X10 + X11 + 3X12) mod 10
If x13 =10, then the check digit is 0.
Example 1
1. Determine the check digit for the book “Larry Can’t Cook”: 978-971-272769- 6?
Ans. 10- (154 mod 10)
=10-4
=6
2. Determine if the ISBN code 978-971-27-2770-2 is valid or not. VALID
UNIVERSAL PRODUCT CODE (UPC)
- A 12-digit code that usually accompanies the bar
code of a product.
Formula:
X12 = 10 – (3X1 + X2 + 3X3 + X4 + 3X5 + X6 + 3X7 + X8 + 3X9 +
X10 + 3X11) mod 10
Check digit=0
CREDIT CARDS
- Normally having a 16-digit numbers 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 to the last digit (the
last digit being the check digit) and summing up all the
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.
Determine which credit card number is valid and which is
not.
a. 5234 8213 3410 1298
b. 6011 0123 9145 2317
Solution:
5 2 3 4 8 2 1 3 3 4 1 0 1 2 9 8
10 2 6 4 16 2 2 3 6 4 2 0 2 2 18 8
Sum=1+0 +2 +6 +4 +1 +6 +2 +2 +3 +6 +4 +2 +0 +2 +1 +8 +8
=60 ≡ 0 mod 10; the indicated credit card number is valid