Mathematics in Management Science Check Digits Examples BINs Codabar Mathematics in Management Science Spring 2015

Check Digits Start with pre-id number. Use this to calculate check digit. Get id number. Sender calculates (via appropriate scheme) check digit and transmits the id number. Receiver uses check digit to detect errors (and fraud). (direct vs indirect)

BIN – aka Bank Routing Numbers Length of ID: 8 + check digit a1a2a3a4a5a6a7a8 c Calculating check digit: c = 7a1+3a2+9a3+7a4+3a5+9a6+7a7+3a8 mod 10 Errors detected/not detected: All single digit errors & 87% of other errors. A direct weighted division by 10 scheme (with wts 7, 3, 9).

Example Find check digits for the Bank routing number 02601288c. Weights are 73973973. Weighted sum of all these is 6+54+3+18+56+24=161 So c =161 mod 10 =1. The complete routing number is 026012881.

Example Find check digits for the Bank routing number 05300021c. Weights are 73973973. Weighted sum of all these is 15+27+14+3=59 So c = 59 mod 10 = 9. The complete routing number is 053000219.

Codabars: Credit Cards Length of ID: 15 + check digit a1a2a3a4a5a6a7a8 a9a10a11a12a13a14a15 c Calculating check digit: Let S = 2a1+a2+2a3+a4+2a5+a6+2a7+a8 +2a9+a10+2a11+a12+2a13+a14+2a15 Let T be number of 2-digit summands in S. Choose c so that S + T + c ends in 0. Errors detected/not detected: All single digit errors & 98% of other errors.

Find check digits for credit card number Example Find check digits for credit card number 4719 2688 1045 710c. Wts 2121 2121 2121 212 Wtd sum S = 8+7+2+9+4+6+16+8+2+8+5+14+1= 90. Then T = 2 , and S + T + c = 92 + c, so c = 8 . The complete credit card number is 4719 2688 1045 7108.

What is a bar code? ZIP Code Bar Codes UPC Bar Codes AirLine Bar Codes Mathematics in Management Science Spring 2015

Bar Codes Enables automated data collection; machine readable. Id number is changed into a bar code. Decoded using optical scanner--beam of light passes over the code Scanner detects differences in reflection intensities (black vs. white bars). These converted to string of 0’s&1’s that represent numbers and letters. These strings give binary code. Bar Code – dark bars and light spaces that encode characters Binary Code – system that represents data with only two symbols

ZIP Codes Id nos that encode geographic data 1963 USPS numbered every post office with 5-digit ZIP code — 0 for points far east, — 9 for points west. 1983 USPS added four digits to get ZIP + 4 code.

All single digit errors; no transppositions. ZIP + 4 Codes Length of ID: 9 + check digit a1a2a3a4a5a6a7a8 a9 c Calculating check digit: Choose c so that a1+a2+a3+a4+a5+a6+a7+a8 a9+c ≡ 0 mod 10. That is, pick c so that above sum ends in 0. Only see c in the bar code! Errors detected/not detected: All single digit errors; no transppositions.

Example Find the check digit for the ZIP+4 code: 45221-0025. 4+5+2+2+1+0+0+2+5+c = 21+c Therefore, c = 9 .

ZIP Code Bar Codes Called Postnet code; simplest bar code.

Check digit chosen so the sum all digits is divisible by 10. POSTNET Bar Codes Encodes ZIP code digits plus a check digit. Table gives code. Every pattern has 3 short bars 2 long bars Check digit chosen so the sum all digits is divisible by 10.

UPC Bar Code UPC bar codes first used on grocery items in 1973; has since spread to most retail products.

UPC Bar Code

Other Bar Codes POSTNET and UPC bar codes are human-readable. Airline bar codes and Intelligent Mail bar codes purely machine readable.

IM Bar Codes 65 bars of different length. Each bar in one of 4 possible states: A short bar (tracker) A medium length bar up (ascender) A medium length bar down (descender) A long bar (full bar).

IM Bar Codes

Coding License Numbers Some states assign driver’s license numbers that encode personal data. Personal data that may be encoded are name, sex, and date of birth. Coding license numbers solely from personal data enables automobile insurers, government entities, and law enforcement agencies to determine the number from the personal data.

Social Security Numbers No personal data encoded in SSN. Social Security numbering scheme predates computers. The only personal information can be deduced from SSN is where holder obtained it. The first three digits show (the state usually) where the applicant applied, with a few exceptions.