1.0       INTRODUCTION

In every publication made in the world, there has to be the identification of the book. This has been attained by the use of many systems which enables the identification of the work that has been done. One of the most used system and that which has managed to attain the standard of the publishing industry is that of the International Standard Book Number system. This has faced many revolutions as from the use of 9 digits to the present use of 13 digits.  This is a unique system of identifying the origin of a particular book together with the author. It was established was the book numbering system which had been introduced in the United Kingdom by Whitaker, J. & Sons limited in 1967 this had 9 digits but the ISBN as revolved to comprise 10 digits of identification. With this, we will deal with the structure of the system, its advantage to the community and the check digits that are normally used together with the change in the system.

2.0       LITERATURE REVIEW

This is one of the systems that have had more influence in the publication industry for its identification of the work in the market. The identification is done on every work being done together with their editions, in doing this; the reprints of the work are usually excepted form the system. This paper will mainly discuss on the advantages of the system to the society, the structure of the system together with its check digits. In doing this, we will be able to understand the mathematics behind the system in the publishing industry.

2.1             ADVANTAGES OF ISBN SYSTEM

With the ability to be able to identify the published work in the society, the system has had many advantages as discussed below.

1.                  It has enabled the saving of time and staff in the industry. This has also prevented the ability of copying other authors work during publishing process.

2.                  It allows for the compilation and updating of the information about the book, thus improving the ability to access the information about a particular book at any time.

3.                  It has facilitated the process of ordering and distribution of books to other locations.

4.                  It assists in the monitoring the sales of the books in the market.

These advantages of the ISBN have encouraged the publishers in the use of the system in the numbering of their works before releasing them to the market for sell. With this, it has avoided the republication of the same work but with different authors.

2.2             STRUCTURE OF ISBN SYSTEM

In the coming up with the number to be assigned to the book, the system is broken up into four main parts, these parts are the structure of the ISBN that will enable one to be able to identify the book that he or she needs to use, buy or sell to the market. ISBN consists of ten digits and later on proceeded with the name ISBN, the ten digits are further divided into four parts of which each part is separated from the other by the use of hyphen or space (Diaz, A. Z.1967, pg 665). To illustrate this clearly, the paper will use one example of a particular book having the following ISBN number: ISBN 0 571 08989 5 or ISBN 90-70002-04-3 these represents the ISBN number of the book the 10 digits and 13 digits respectively.

These parts consist of the group identifier, the publisher identifier, the title identifier and the check digit. The numbers in each of these parts differs from one another depending on the quantity of titles intended to be created by the publisher group. Thus, the larger the publisher group the fewer the digits used in the parts. As the parts will be discussed below, the paper will be referring to the example given earlier in the text.

2.2.1      Group Identifier

This is the first part of the ISBN and it normally identifies the country, area and language that participate in the system. This may consist of up to 5 digits depending on the quantity of title of that particular publisher. In the example above, the group identifier is ISBN 90….

2.2.2      Publisher Identifier

This is the second part of the number and it is usually used to identify the publisher within the group, it gives the exact name, location in term of the house and their address so that they can be accessed easily in time of need if problem arises. This number goes up to seven digits depending on the type of the publisher group. It is normally offered out to the publisher by the ISBN group agency that is accountable for the supervision of the ISBN system within the nation where the publisher is formally based. In the example above, the publisher identifier number will be: ISBN 90-70002-….

2.2.3      Title Identifier

This part of the ISBN tries to identify the precise version of the publication for a give publisher in the market. It consists of up to six digits. Since the ISBN has to have ten digits, the missing digits are normally represented by zero in the numbering system. In the case of our example, the title identifier will be ISBN 90-70002-04, thus, 04 is the précised version of the publication.

2.2.4      Check Digit

This is normally the last digit in the ISBN system. It is attained by calculating on a modulus 11 with weight 10-2, making use of X in lieu of 10. This means that, the nine digits attained earlier have to be multiplied by a number between 10-2 to give the sum of the products that is divisible by 11 when the check digit is added onto it. Thus in the above used example, the check digit will be ISBN 90-70002-04-3

The above check digit given is from the ISBN 10 digit system, in this system, the check digit ranges from 0 to 10 and whenever 10 is to be used, the symbol X is used instead. This is normally calculated just as stated above, for example for the check digit for the ISBN-10 of 0-306-40615- will be calculated as follows;

=0*10+3*9+0*8+6*7+4*6+0*5+6*4+1*3+5*2

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

=130

=130/11 =11 remainder 9

=11-9

 =2 (check digit)

Therefore the check digit will be 2 giving complete ISBN of 0-306-40615-2

In the calculation of the ISBN -13 check digit, they make use of the first 12 digits only minus the check digit itself, then, these digit is multiplied by 1 or 3 alternately staring for left to right, the products are summed up and divided by 10 to give a value between 0 and 9 then the value is subtracted from 10 giving a value between 1 and 10. For instance, for the ISBN-13 check digit of 978-0-306-40615- it will be calculated as follows;

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 (check digit)

Therefore the complete ISBN number will be ISBN 978-0-306-40615-7

With the knowledge of these parts of the system, the industry has been able to attain the use of the 13 digits system so as to have the two-fold within the system. With any of the number of digit used, it is only the check digit which varies a lot.

CONCLUSION

ISBN has all the factors to be able to identify all the publication being done in any nation, thus facilitating the publishing process in the industry.

REFERENCE

Diaz, A. J. (1967) Guide to reprints pp 664-667 Washington DC: University of Michigan ISBN 0918086213 or 9780918086211