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

2. 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)

3. 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).

4. Example
Find check digits for the Bank routing number c. Weights are Weighted sum of all these is =161 So c =161 mod 10 =1. The complete routing number is

5. Example
Find check digits for the Bank routing number c. Weights are Weighted sum of all these is =59 So c = 59 mod 10 = 9. The complete routing number is

6. 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.

7. Find check digits for credit card number
Example
Find check digits for credit card number c.
Wts
Wtd sum
S = = 90. Then T = 2 , and S + T + c = 92 + c, so c = 8 .
The complete credit card number is

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

9. 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

10. 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.

11. 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.

12. Example
Find the check digit for the ZIP+4 code: c = 21+c Therefore, c = 9 .

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

14. 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.

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

16. UPC Bar Code

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

19. 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).

20. IM Bar Codes

22. 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.

23. 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.