Author: Fernando Silva
ISBNs (or International Standard Book Numbers) are mystical code numbers that
uniquely identify books. The purpose of this article is to remove the mystery
surrounding the structure of the ISBN, allowing applications to perform data
validation on entered candidate ISBNs.
Answer:
ISBNs are composed of thirteen characters, limited to the number characters "0"
through "9", the hyphen, and the letter "X". This thirteen-character code is
divided into four parts, each separated by hyphens: group identifier, publisher
identifier, book identification for the publisher, and the check digit. The first
part (group identifier) is used to identify countries, geographical regions,
languages, etc. The second part (publisher identifier) uniquely identifies the
publisher. The third part (book identifier) uniquely identifies a given book within
a publisher's collection. The fourth and final part (check digit) is used with the
other digits in the code in an algorithm to derive a verifiable ISBN. The number of
digits in the first three parts of an ISBN may contain a variable number of digits,
but the check digit will always consist of a single character (between "0" and "9",
or "X" for a value of 10) and the
ISBN as a whole will always consists of thirteen characters (ten numbers plus the
three hyphens dividing the four parts of the ISBN).
The ISBN 3-88053-002-5 breaks down into the parts:
Group: 3
Publisher: 88053
Book: 002
Check Digit: 5
An ISBN can be verified to be a valid code using a simple mathematical algorithm.
This algorithm takes each of the nine single digits from the first three parts if
the ISBN (sans the non-numeric hyphens), multiplies each single digit by a number
that is less than eleven the number of positions from the left each digit that is
in the ISBN, adds together the result of each multiplication plus the check digit,
and then divides that number by eleven. If that division by eleven results in no
remainder (i.e., the number is modulo 11), the candidate ISBN is a valid ISBN. For
example, using the previous sample ISBN 3-88053-002-5:
ISBN: 3 8 8 0 5 3 0 0 2 5
Digit Multiplier: 10 9 8 7 6 5 4 3 2 1
Product: 30+72+64+00+30+15+00+00+04+05 = 220
Since 220 is evenly divisible by eleven, this candidate IDBN is a valid ISBN code.
This verification algorithm is easily translated into Pascal/Delphi code.
String manipulation functions and procedures are used to extract the check digit
and the remainder of the ISBN from the String type value passed to a validation
function. The check digit is converted to Integer type, which forms the start value
of the aggregate variable onto which the multiplication of each digit in the
remainder of the ISBN (the single digits that comprise the first three parts of the
ISBN) will be added. A For loop is used to sequentially process each digit in the
remainder, ignoring the hyphens, multiplying each digit times its position in the
ISBN remainder relative to the other digits in the remainder. The final value of
this aggregate variable is then checked to see whether it is evenly divisible by
eleven (indicating a valid ISBN) or not (indicating an invalid candidate ISBN).
Here is an example of this methodology applied in a Delphi function:
1
2 function IsISBN(ISBN: string): Boolean;
3 var
4 Number, CheckDigit: string;
5 CheckValue, CheckSum, Err: Integer;
6 i, Cnt: Word;
7
8 begin
9 // Get check digit
10 CheckDigit := Copy(ISBN, Length(ISBN), 1);
11 // Get rest of ISBN, minus check digit and its hyphen
12 Number := Copy(ISBN, 1, Length(ISBN) - 2);
13 // Length of ISBN remainder must be 11 and check digit between 9 and 9 or X
14 if (Length(Number) = 11) and (Pos(CheckDigit, '0123456789X') > 0) then
15 begin
16 // Get numeric value for check digit
17 if (CheckDigit = 'X') then
18 CheckSum := 10
19 else
20 Val(CheckDigit, CheckSum, Err);
21 // Iterate through ISBN remainder, applying decode algorithm
22 Cnt := 1;
23 for i := 1 to 12 do
24 begin
25 // Act only if current character is between "0" and "9" to exclude hyphens
26 if (Pos(Number[i], '0123456789') > 0) then
27 begin
28 Val(Number[i], CheckValue, Err);
29 // Algorithm for each character in ISBN remainder, Cnt is the nth character
30 // so processed
31 CheckSum := CheckSum + CheckValue * (11 - Cnt);
32 Inc(Cnt);
33 end;
34 end;
35 // Verify final value is evenly divisible by 11
36 if (CheckSum mod 11 = 0) then
37 IsISBN := True
38 else
39 IsISBN := False;
40 end
41 else
42 IsISBN := False;
43 end;
This is a simplified example, kept simple to best demonstrate the algorithm to decode ISBNs. There are a number of additional features that would be desirable to add for use in a real-world application. For instance, this example function requires the candidate ISBN be passed as a Pascal String type value, with the hyphens dividing the four parts of the ISBN. Added functionality might accommodate evaluating candidate ISBNs entered without the hyphens. Another feature that might be added is checking that ensures three hyphens are properly included, as opposed to just thirteen number characters.
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