2988:How to Validate ISBNs
KEYWORDS: ISBN VALIDATION ALGORITHM AREA: General
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.
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:
function IsISBN(ISBN: String): Boolean;
var
Number, CheckDigit: String;
CheckValue, CheckSum, Err: Integer;
i, Cnt: Word;
begin
{Get check digit}
CheckDigit := Copy(ISBN, Length(ISBN), 1);
{Get rest of ISBN, minus check digit and its hyphen}
Number := Copy(ISBN, 1, Length(ISBN) - 2);
{Length of ISBN remainder must be 11 and check digit between 9 and 9 or
X}
if (Length(Number) = 11) and (Pos(CheckDigit, '0123456789X') > 0) then
begin
{Get numeric value for check digit}
if (CheckDigit = 'X') then
CheckSum := 10
else
Val(CheckDigit, CheckSum, Err);
{Iterate through ISBN remainder, applying decode algorithm}
Cnt := 1;
for i := 1 to 12 do begin
{Act only if current character is between "0" and "9" to exclude
hyphens}
if (Pos(Number[i], '0123456789') > 0) then begin
Val(Number[i], CheckValue, Err);
{Algorithm for each character in ISBN remainder, Cnt is the nth
character so processed}
CheckSum := CheckSum + CheckValue * (11 - Cnt);
Inc(Cnt);
end;
end;
{Verify final value is evenly divisible by 11}
if (CheckSum MOD 11 = 0) then
IsISBN := True
else
IsISBN := False;
end
else
IsISBN := False;
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.
TI
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