How to sell

modular arithmetic to students only interested in literature? Well, try

to explain the structure of ISBN-numbers

“The ISBN (International Standard Book Number) is a unique

machine-readable identification number, which marks any book

unmistakably. This number is defined in ISO Standard 2108. The number

has been in use now for 30 years and has revolutionised the

international book-trade. 166 countries and territories are officially

ISBN members. The ISBN accompanies a publication from its production

onwards.” The ISBN-number of a book is a ten-digit number divided into

four parts, separated by hyphens telling you a lot about the ambitions

and location of the book’ publisher. I’ll explain some of it by

telling how I obtained the barcode for the first book to be published by

neverendingbooks.org (see

picture). The first part is the group

identifier and identifies a country, area or language area

participating in the ISBN system. For the Netherlands and the Flemish

speaking part of Belgium this identifier is **90**. Hence,

depending on your location you have to approach different agencies in

order to obtain an ISBN-number. If you are living in the US all you have

to do is to invent a name for your PublishingHouse, get your Visa-card

out and visit isbn.org

. For smaller groups the process is more personal. The first time I

tried to apply for an ISBN-number with De Boekenbank I

messed up and got immediately an email telling me what I did wrong. I

replied explaining what NeverEndingBooks had in mind and asked advice on

how to set it up properly. I’m sure I’ll need this personal contact

again in the near future. The second part is the _Publisher

Identifier_ or _prefix_. I didn’t know this before but the

very definition of a _publisher_ is the person or company

registering a book’s ISBN. Hence, if you intend to publish a series of

books your local ISBN-agency has to reserve a certain amount of

ISBN-numbers for you, all having the same start-block (the prefix). The

shorter the prefix the more ambitious the PublishingHouse. The

registered prefix of NeverEndingBooks is **90809390** which

tells the experienced ISBN-watcher that we intend in the next years to

publish “only” ten books. If you have more energy you can also apply

for a series of 100, 1000 or even 10000 ISBN-numbers but the amount of

money needed to register these series increases quickly‚Ä¶ The third

part of the ISBN-number is the _title identifier_ so for our

first book it is just **1**. However, in order to register

it you have to provide the agency (minimally) with a title and

publication date (fortunately, author, price, number of pages etc. are

optional at this stage). Anyway, the first real deadline for

NeverEndingBooks will be may 15th 2005! And now it is time to return

to modular arithmetic, the fourth part is a _check digit_. The

check digit is the last digit of an ISBN. It is calculated on a modulus

11 with weights 10-2, using X in lieu of 10 where ten would occur as a

check digit. This means that each of the first nine digits of the ISBN

excluding the check digit itself is multiplied by a number

ranging from 10 to 2 and that the resulting sum of the products, plus

the check digit, must be divisible by 11 without a remainder. In our

case, we have the following numbers(weights) **9(10) 0(9) 8(8)
0(7) 9(6) 3(5) 9(4) 0(3) 1(2)** We have to multiply the numbers

with their weight and add them all up,

**90+0+64+0+54+15+36+0+2=261=8(mod 11)**whence the check

digit should be

**3**. For example, I know already that the

ISBN-number of the second book to be published by NeverEndingBooks will

be 90-809390-2-1 but, due to lacking information, it will take a while

before it can be registered.