Identification Numbers Chapter 9
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
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
First Attempt at a Modern Id Number Social Security Numbers
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
Postal Money Orders 6+3+0+2+4+3+8+3+8+4=41/9 = 4 R5 R5
Problems? Postal Money Orders Single Digit Errors? #7797 = 7+7+9+7 = 30/9 = 3 R3 #7707 = 7+7+0+7 = 21/9 = 2 R3 Some are found but not all (base 9) Transpositions? 8397 = 8+3+9+7 = 27/9 = 3 R0 8937 = 8+9+3+7 = 27/9 = 3 R0 None are found
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
1960 s Traveler s Checks 3+8+7+5+0+5+0+5+5+7 3+8+7+5+0+5+0+5+5+7 = = 45/9 45/9 = = 5 5 R0 R0
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
Euro X=7 X=7 7+1+1+8+3+8+0+6+5+3+8+4=54/9=R0
Problems? Traveler s Checks Single Digit Errors? #7794 = 7+7+9+4 = 27/9 = 3 R0 #7704 = 7+7+0+4 = 18/9 = 2 R0 Some are found but not all Transpositions? 8397 = 8+3+9+7 = 27/9 = 3 R0 8937 = 8+9+3+7 = 27/9 = 3 R0 None are found
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
1826883993 3 7 1278818795 32 1970 s Airline Tickets 57 07 56 18 14 48 42 61 56 58 56 27 21 69 63 65 63 23 21 22 21 1
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 R0 1281 = 1281/7 = 183 R0 Many are caught but not all
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
UPC Code 54 5430 3000 0021 2103 0319 19 5+3+0+2+0+1=11 5+3+0+2+0+1=11 x 3 = 33 33 4+0+0+1+3+9= 4+0+0+1+3+9= 17 17 50 50
Problems? UPC code Problems Single Digit Errors? All Found Transpositions? 89% found but not All
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
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 7-3-9 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
Bank Checks Weights Weights 7-3-9 7-3-9 (0x7)+(7x3)+(1x9)+ (0x7)+(7x3)+(1x9)+ (0x7)+(0x3)+(0x9)+ (0x7)+(0x3)+(0x9)+ (0x7)+(1x3) (0x7)+(1x3) = 33 33
Bank Check Problems Problems? Single Digit Errors? All Found Transpositions? Most but not All
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
First Digit = Credit Cards - cont =1 American Express =2 Diners Club =3 - American Express =4 Visa =5 MasterCard =6 - Discover
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
Credit Cards 4128 41280012 00123456 34567890 4+2+0+1+3+5+7+9 4+2+0+1+3+5+7+9 = 31 31 x 2 = 62 62 1+1+1 1+1+1 = 3 1+8+0+2+4+6+8+0 1+8+0+2+4+6+8+0 = 29 29 94 94
Credit Cards Make it Good! 4128 41280012 00123456 34567890 4+2+0+1+3+5+7+9 4+2+0+1+3+5+7+9 = 31 31 x 2 = 62 62 1+1+1 1+1+1 = 3 1+8+0+2+4+6+8+0 1+8+0+2+4+6+8+0 = 29 29 94 94 +? +? = 100 100
Problems? Credit Card Problems Single Digit Errors? All Found Transpositions? 98% but not All
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
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
ISBN (0*10)+(7*9)+(1*8)+(6*7)+(7*6)+(4*5)+(7*4)+(8*3)+(3*2)+(9*1)= 0 + 63 63 + 8 + 42 42 + 42 42 + 20 20 + 28 28 +24 +24 + 6 + 9 = 242 242 242/11 242/11 = 22 22 (no (no remainder) remainder)
ISBN (0*10)+(7*9)+(1*8)+(6*7)+(7*6)+(3*5)+(8*4)+(1*3)+(7*2)+(1*1)= 0 + 63 63 + 8 + 42 42 + 42 42 + 15 15 + 32 32 + 3 + 14 14 + 1 = 220 220 220/11 220/11 = 20 20 (no (no remainder) remainder)
ISBN cont. (0*10)+(8*9)+(3*8)+(8*7)+(4*6)+(4*5)+(5*4)+(7*3)+(3*2)+(?*1)= 0 + 72 72 + 24 24 + 56 56 + 24 24 + 20 20 + 20 20 + 21 21 + 66 +? = 243 243 243/11 243/11 = 22+ 22+ 23*11 23*11 = 253 253 253-243 253-243 = 10 10
ISBN cont. (0*10)+(8*9)+(3*8)+(8*7)+(4*6)+(4*5)+(5*4)+(7*3)+(3*2)+(X*1)= 0 + 72 72 + 24 24 + 56 56 + 24 24 + 20 20 + 20 20 + 21 21 + 6 + 10 10 = 253 253 253/11 253/11 = 23 23 (no (noremainder)
Adding to Modern Id Numbers Unambiguous Self Checking Area Location Zip Codes!!
Adding to Modern Id Numbers
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
Algorithm: Zip Codes Add all digits in the zip code (including the check digit) Divide sum by 10 If no remainder = good zip code
Zip Codes All Zip numbers are made up of a combination of 3 short and 2 long bars
Zip Code Format
Zip Codes