ISBN: a)1, a)2, ... , a)10 _ a)1 + 2*a)2 + 3a)3 + ... + 9a)9 + 10a)10 = 0 (mod 11) _______________________________________________________________________________ UPC: 12 digits - x-xxxxx-xxxxx-x _ 3 * (sum of odd position digits) + (sum of even position digits) = 0 (mod 10) _______________________________________________________________________________ "Bone" multiplication 4 3 2 __________ 1 |0/|0/|0/| 2 |/8|/6|/4| |ŻŻŻŻŻŻŻŻ| 0 |2/|1/|1/| 5 432 * 25 = 10800 |/0|/5|/0| ŻŻŻŻŻŻŻŻŻŻ 8 0 0