This question's explanation and your answers so far.
問98
頻出度★★☆
多くの市販の書籍には，書籍を識別するための ISBN（International Standard Book Number）コードが付けられている。ISBN コードは，0～9の数字を使った13桁の記号で構成され，左側から桁を数える。最も左側の桁を1桁目とする。1桁目から12桁目までは，国記号，出版者記号及び書籍固有の記号などが含まれる。
ISBN コードの13桁目（最も右側の桁）はチェック数字と呼ばれる桁である。ISBN コードのチェック数字は，1桁目から12桁目の数字を使って，次の計算方法によって求める。ここで，図1のように1桁目から12桁目の数字を a₁～a₁₂，チェック数字を X とする。
〔チェック数字の計算方法〕
(1) a₁～a₁₂について，奇数桁には1，偶数桁には3の重みを付ける。
(2) a₁～a₁₂の各桁に，それぞれの桁に対応した重みを掛けたものの和 S を求める。
S ＝ a₁×1＋a₂×3＋a₃×1＋…＋a₁₂×3
(3) S を10で割った余り R を求める。
(4) 10から R を引いた値をチェック数字 X とする。なお，この値が10になった場合は，チェック数字は0とする。
ISBN コードにチェック数字が含まれていることによって得られる効果はどれか。
出典 平成24年度 春期 ITパスポート試験 問98
解説
問 98
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○ア
正解The correct answer is ア. A check digit is a digit reserved for checking, calculated from the digits of the code itself by a fixed rule and appended at the end. As the preamble of question group D states, an ISBN code has 13 digits: digits 1 through 12 hold the country code, the publisher code, the book-specific code and so on, and only the 13th digit is used as the check digit. It is obtained like this: (1) weight digits 1 to 12 by 1 for odd positions and 3 for even positions; (2) take the sum S of each digit multiplied by its weight; (3) find the remainder R of S divided by 10; (4) subtract R from 10 to get the check digit X — but, as the proviso in the original text says, if this value becomes 10 (that is, when R is 0), the check digit is taken as 0. The important point here is that X is a value determined uniquely by digits 1 to 12. So when a person enters an ISBN code by hand, if even one digit is mistyped, the check digit recalculated from the entered digits 1 to 12 will disagree with the entered 13th digit, and the machine can point out on the spot that “the input is wrong.” This is exactly the effect ア describes — “a checking function is added, so input errors are easier to detect when a person enters an ISBN code” — and it is the very purpose of providing a check digit.
×Incorrectイ
What identifies a book uniquely is the country code, publisher code and book-specific code in digits 1 to 12 mentioned in the preamble, not the check digit in digit 13. The check digit is a redundant digit computed from the remaining 12 digits, so in itself it carries not even one bit of new identifying information (a book can still be identified with the check digit removed). Therefore, improving the efficiency of computer processing in inventory management systems and book search systems is an effect of adopting the ISBN code itself, not an effect gained from the code containing a check digit.
×Incorrectウ
The check digit is only a single check value from 0 to 9; it carries no information expressing an order such as title, author or genre. Its value is determined by the remainder of the weighted sum of digits 1 to 12, so there is no guarantee that books with similar content get similar check digits, and sorting by it would not produce any meaningful arrangement. Besides, which shelf a book is displayed on in a bookstore is decided by each store's own display policy, and has nothing to do with the last digit of the ISBN code.
×Incorrectエ
The book classification that libraries and schools use for managing books is done with a classification system separate from ISBN, such as the Nippon Decimal Classification (NDC); it is not something the check digit of the ISBN code provides. Within an ISBN, what expresses divisions such as the publisher is the country code and the publisher code, and both of them are contained in digits 1 to 12. The 13th digit, the check digit, carries no classification meaning at all, so adding it does not make book classification any clearer.
ここがポイント
A check digit is a digit used for checking, derived from the digits of the code itself by a fixed calculation rule and appended at the end; its purpose is limited to “detecting” input errors or reading errors (it cannot correct them). In ISBN-13, digits 1 to 12 are multiplied by the weights 1, 3, 1, 3, …, the remainder R of the sum S divided by 10 is found, and the check digit is X = 10 − R; if this value becomes 10, X is taken as 0.
Questions about coding systems are sorted out by asking which digit plays which role. In ISBN, identification is handled by digits 1 to 12 (country code, publisher code, book-specific code), book classification is handled by a separate system outside ISBN such as NDC, and the 13th digit, the check digit, is used only for checking. Once you grasp that these roles do not overlap, every choice that talks about identification, sorting or classification can be ruled out.