Question

Determine whether the check digit of the ISBN-10 for this textbook (the seventh edition of Discrete Mathematics and its Applications) was computed correctly by the publisher.

Short answer

The check digit was computer correctly

Step-by-step solution

Step 1

The book's ISBN is:$\mathbf{0073383090}$

ISBN-11 code: 123456789X

Since we know the ISBN for the book and we also know the verification code for ISBN-11, we have to check that the code is congruent to$\mathbf{0}\mathbf{(}\mathbf{mod}\mathbf{11}\mathbf{)}$

Step 2

$\mathbf{0}\mathbf{\ast }\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{\ast }\mathbf{2}\mathbf{+}\mathbf{7}\mathbf{\ast }\mathbf{3}\mathbf{+}\mathbf{3}\mathbf{\ast }\mathbf{4}\mathbf{+}\mathbf{3}\mathbf{\ast }\mathbf{5}\mathbf{+}{\mathbf{8}}^{\mathbf{\star }}\mathbf{6}\mathbf{+}{\mathbf{3}}^{\mathbf{\star }}\mathbf{7}\mathbf{+}\mathbf{0}\mathbf{\ast }\mathbf{8}\mathbf{+}\mathbf{9}\mathbf{+}\mathbf{9}\mathbf{+}\mathbf{0}\mathbf{\ast }{\mathbf{10}}^{\mathbf{\circ }}\mathbf{0}\mathbf{(}\mathbf{mod}\mathbf{(}\mathbf{11}\mathbf{)}$

We then multiply each digit in the code by every digit in the verification code.

Step 3

Since 198 has a remainder of zero when divided by$\mathbf{11}\mathbf{,}\mathbf{198}$ is then congruent to$\mathbf{0}\mathbf{(}\mathbf{mod}\mathbf{11}\mathbf{)}$