The International Standard Book Number (ISBN) used in many libraries consists of nine digits followed by a tenth check digit (somewhat like Hamming codes), which satisfies
Determine whether each of the ISBN’s below is correct.
(a) 0-07-232569-0 (USA)
(b) 91-7643-497-5 (Sweden)
(c) 1-56947-303-10 (UK)
When printing the ISBN , two unequal digits were transposed. Show that the check digits detected this error.
Remark: Such codes are called error correcting codes and are fundamental to wireless communications including cell phone technologies.