Download Error Detection in Identification Numbers: UPC, ISBN, Bank ID and Bar Codes - Prof. Mingqi and more Study notes Mathematics in PDF only on Docsity! 1 Announcement Math 113 section 21-26 Instructor: M.Xiao •The Third Hour Exam: Nov. 6, Friday in class. Oct. 23, 2009 Help sessions Tuesday and Thursday 6-7:45p.m. Location: agriculture building (AG) 152. Chapter 16 Identification Numbers Modern identification numbers at least have two functions: •identify the person or thing to which it is associated. •have a “self-checking” mechanism of the number Many frequently used types of error-detecting code for identification numbers include an extra digit (usually the last digit) called a check digit. Example Universal Product Code (UPC) The scheme used on grocery products is the so-called Universal Product Code. The UPC adds a check digit at the end by adding the digits and multiplying by their weight (alternately 1 for even positions, 3 for odd positions). The sum must be a number ending in 0 . Example: an UPC number 0 38000 00127 7 Category of goods Manufacturer product Check digit (0+8+0+0+1+7)*3+(3+0+0+0+2+7)*1=60 The sum is a number ending in 0. One of the most efficient error-detection methods:Codabar The Codabar system is a variation of UPC using a similar sum with weights 2 (odd positions) and 1 (even positions). To this sum, add the number of digits in odd positions that exceed 4 ; The resulting number must end in 0 to be a valid Codabar code. (4+2+0+1+3+5+7+9)*2 +(1+8+0+2+4+6+8)*1 +3=94 which does not end in 0, so This credit card is not valid. The International Standard Book Number (ISBN) A correctly coded 10 -digit ISBN has the property that is evenly divisible by 11. 1021 aaa ⋅⋅⋅ 10987654321 2345678910 aaaaaaaaaa +++++++++ Example: the ISBN of our main textbook is 0-7167-4783-9 The initial digit 0 indicates that the book is published in an English -speaking country. The next block 7167 identifies the publisher. The third block 4783 is assigned by the publisher and identifies this book. The last digit, 9, is the check digit. 10*0+9*7+8*1+7*6+6*7+5*4+4*7+3*8+2*3+9=242 Notice 242/11=22. So 242 is evenly divisible by 11. Old Exam Question Determine the check digit which should be appended to ISBN 0-7167-9811. __A. 2 __B. 5 __C. 6 __D. 8 10*0+9*7+8*1+7*6+6*7+5*9+4*8+3*1+2*1+X = 237 +X 237=11*21+6 Thus X=5 2 Bank Identification Number Each bank has an eight-digit identification number: 8321 aaaa L 87654321 37937937 aaaaaaaa +++++++ The check digit is the last digit of In this example, the bank ID is 07100001 331307090307197307 =⋅+⋅+⋅+⋅+⋅+⋅+⋅+⋅ Bar CodesBar Codes ZIP+4 bar code Caaa 921 ⋅⋅⋅ Then the sum Caaa ++⋅⋅⋅++ 921 ends with 0. 6+0+5+1+5+9+9+6+8+1=50The sum is a number ending in 0. Bar Codes Chapter 7 Data for Decision Numbers are in a myriad of ways to describe the world we live in. Our social and economic concerns, science and ecology, politics, religion, health, recreation, any area of human activity is better understood by the collection and analysis of data. Objectives of This Chapter 1. How to produce trustworthy data; 2. How to draw reliable conclusions from the data; This is the role of statistics , the science of data handling. Sample and Population In statistical studies, we gather information about a small, partial group (a sample) in order to draw conclusions about the whole, large group we are interested in (the population). The entire group of individuals that we want information about is called the population. A sample is a part of the population that we actually examine in order gather information. Definitions:
