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Calculating the ISBN Number

The International Standard Book Number (ISBN) is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster.

We can check if they are correct by multiplying each digit by 1/3 alternating between each number except the last number. 

The ISBN number can be either 10 check digits or 13 check digits.

-ISBN-13 check digit: 

**The ISBN-13 check digit of 978-0-306-40615-? is calculated as follows:

s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3

  =   9 +  21 +   8 +   0 +   3 +   0 +   6 +  12 +   0 +  18 +   1 +  15

  = 93

93 / 10 = 9 remainder 3

10 –  3 = 7

Therefore, we now know that the last digit is 7 and the complete sequence is ISBN

 978-0-306-40615-7.

-ISBN-10 check digit:

Each of the first 9 digits of the1 0-digit ISBN – excluding the check digit– will be multiplied by sequence number between 10-2, and the remainder of the sum, with respect to 11, is computed. The remainder, plus the check digit, should be equal to 11. Thus, the check digit is 11 minus the remainder of the sum of the products.

**The ISBN-10 check digit of of 0-306-40615-? is calculated as the following:

s=(0x10)+(3x9)+(0x8)+(6x7)+(4x6)+(0x5)+(6x4)+(1x3)+(5X2)

=0+27+0+42+24+0+24+3+10

=130=12x11-2

Thus the check digit is 2, and the complete sequence is ISBN 0-306-40615-2. The value "X" required to satisfy this condition might be 10; if so, an 'X' should be used.

**The ISBN-10 check digit can be converted to ISBN-13 check digit.**