Identification Numbers. Chapter 9

Transcription

1 Identification Numbers Chapter 9

2 Modern Id Numbers - Functions 1. Unambiguous Identify the person or thing to which it is associated 2. Must have a Self checking aspect to the number

3 Modern Id Numbers Common Errors 1. Single Digit Errors e.g. mistake a 3 for an 8 2. Transpositions of digits next to each other e.g. 83 transposed to 38

4 First Attempt at a Modern Id Number Social Security Numbers

5 1950 s Postal Money Orders Algorithm: Add all of the digits except the last Divide answer by 9 If the remainder is the same as the last digit of the money order valid number

6 Postal Money Orders =41/9 = 4 R5 R5

7 Problems? Postal Money Orders Single Digit Errors? #7797 = = 30/9 = 3 R3 #7707 = = 21/9 = 2 R3 Some are found but not all (base 9) Transpositions? 8397 = = 27/9 = 3 R = = 27/9 = 3 R0 None are found

8 1960 s Traveler s Checks Algorithm: Add all of the digits in the number (including the check digit) Divide result by 9 If no remainder Valid Number

9 1960 s Traveler s Checks = = 45/9 45/9 = = 5 5 R0 R0

10 2000 s Euro Currency Algorithm: Convert letter (issuing country code to number) Add all of the digits in the number (including the check digit) Divide result by 9 If no remainder Valid Number

11 Euro X=7 X= =54/9=R0

12 Problems? Traveler s Checks Single Digit Errors? #7794 = = 27/9 = 3 R0 #7704 = = 18/9 = 2 R0 Some are found but not all Transpositions? 8397 = = 27/9 = 3 R = = 27/9 = 3 R0 None are found

13 Algorithm: 1970 s Airline Tickets Divide entire number, except for the last digit by 7 Remainder of the division will be the check digit (valid airline ticket) Same Algorithm is used for UPS, Federal Express, Airborne, and other related transportation companies

14 s Airline Tickets

15 Problems? Airline Tickets Single Digit Errors? #4562 = 4562/7 = 651 R5 #4569 = 4569/7 = 652 R5 Most are caught but not all Transpositions? 1218 = 1218/7 = 174 R = 1281/7 = 183 R0 Many are caught but not all

16 1970 s UPC Code UPC (Universal Product Code) is 12 digits First Digit = Category of Goods Next Five Digits = Manufacturer number Next Five Digits = unique product Id Last Digit = Check Digit

17 UPC Code = =11 x 3 = = =

18 Problems? UPC code Problems Single Digit Errors? All Found Transpositions? 89% found but not All

19 UPC Code Algorithm: 1. Add all of the digits in the odd positions of the code 2. Triple the results of step 1 3. Add all the digits in the even positions of the code 4. Add results of steps 2 and 3 5. If result of step four ends in 0 = valid number

20 1960 s Bank Checks Bank Id Numbers are 9 digits First 8 digits are to identify the bank Last digit is the check digit Algorithm: 1. Apply the weights to the 8 bank id digits 2. Sum the result of the weight application 3. Answer in the form XY 4. Y= check digit = valid bank check

21 Bank Checks Weights Weights (0x7)+(7x3)+(1x9)+ (0x7)+(7x3)+(1x9)+ (0x7)+(0x3)+(0x9)+ (0x7)+(0x3)+(0x9)+ (0x7)+(1x3) (0x7)+(1x3) = 33 33

22 Bank Check Problems Problems? Single Digit Errors? All Found Transpositions? Most but not All

23 Credit Cards Format (for 16 digit cards): First Digit = type of card Next Four digits = issuing bank Next Eight Digits = unique member id Last Digit = Check Digit

24 First Digit = Credit Cards - cont =1 American Express =2 Diners Club =3 - American Express =4 Visa =5 MasterCard =6 - Discover

25 Credit Cards Algorithm: 1. Add Digits in the odd positions 2. Double sum of step 1 3. Count digits in the odd positions that are greater than 4 4. Add digits in the even positions 5. Sum results of steps 2,3,and 4 6. Result of step five in form XY if Y=0 valid credit card number

26 Credit Cards = x 2 = = =

27 Credit Cards Make it Good! = x 2 = = = ? +? =

28 Problems? Credit Card Problems Single Digit Errors? All Found Transpositions? 98% but not All

29 Format: ISBN (International Standard Book Number) First Digit Book published in _ speaking country Next Block of 4 Publisher id number Net Block of 4 Assigned by publisher to identify book Last Digit check digit

30 Algorithm: ISBN (International Standard Book Number) Apply the weights 10, 9 1 to the ISBN digits E.g. (10*d 1 )+ (9*d 2 )+ (8*d 3 )+ (1*d 10 ) Divide sum by 11 If no remainder good number E.g. Last Digit could be X

31 ISBN (0*10)+(7*9)+(1*8)+(6*7)+(7*6)+(4*5)+(7*4)+(8*3)+(3*2)+(9*1)= = /11 242/11 = (no (no remainder) remainder)

32 ISBN (0*10)+(7*9)+(1*8)+(6*7)+(7*6)+(3*5)+(8*4)+(1*3)+(7*2)+(1*1)= = /11 220/11 = (no (no remainder) remainder)

33 ISBN cont. (0*10)+(8*9)+(3*8)+(8*7)+(4*6)+(4*5)+(5*4)+(7*3)+(3*2)+(?*1)= ? = /11 243/11 = *11 23*11 = = 10 10

34 ISBN cont. (0*10)+(8*9)+(3*8)+(8*7)+(4*6)+(4*5)+(5*4)+(7*3)+(3*2)+(X*1)= = /11 253/11 = (no (noremainder)

35 Adding to Modern Id Numbers Unambiguous Self Checking Area Location Zip Codes!!

36 Adding to Modern Id Numbers

37 Zip Codes Format: First Digit one of 10 geographical areas Next 2 digits central mail distribution point (sectional center) Next 2 digits town or local post office alphabetical within delivery area Except largest city given 01 Last Digit = check digit

38 Algorithm: Zip Codes Add all digits in the zip code (including the check digit) Divide sum by 10 If no remainder = good zip code

39 Zip Codes All Zip numbers are made up of a combination of 3 short and 2 long bars

40 Zip Code Format

41 Zip Codes