1. Chapter 16: Identification Numbers Lesson Plan
For All Practical Purposes
Identification Numbers
Check Digits
The ZIP Code
Bar Codes
Encoding Personal Data
Mathematical Literacy in Today’s World, 7th ed. 1
© 2006, W.H. Freeman and Company

2. Chapter 16: Identification Numbers Identification Numbers
Modern identification numbers serve at least two functions:
The number should unambiguously identify the person or thing with which it is associated .
The number should have a “self-checking” aspect.
Code
A group of symbols that represent information.
Codes have been invented for storing, securing, and transmitting information.
Examples: Hieroglyphics, the Greek alphabet, Roman numerals, Morse code, and the “genetic code” used to describe DNA 2

3. Chapter 16: Identification Numbers Check Digits
A digit included in an identification number for the purpose of error detection.
Mathematical calculations or schemes are used on the digits of the identification number to assign the check digit.
Computers use the check digit to help detect typing errors during data entry to prevent and detect fraud and to find other errors.
U.S. Postal Service money order with identification number and
check digit 5.
The check digit in this case is the calculated remainder after dividing the sum of the first ten digits by 9. 3

4. Chapter 16: Identification Numbers Check Digits
Universal Product Code (UPC)
A bar code and identification number that are used on most retail items.
By using weighted schemes in the calculation of the check digit, the UPC code can achieve greater error detection—up to 100% of all single-digit errors and most other types of errors.
Example: Consider the number found on the bottom of a box of cornflakes.
The first digit identifies a broad category of goods.
The next five digits identify the manufacturer.
The next five digits identify the product.
The last is a check digit. 4

5. Chapter 16: Identification Numbers Check Digits
Bank Identification Number
Here is what the string of numbers at the bottom of a check mean:
0710 Bank’s Federal Reserve District, office, and state or special collection arrangement
0001 Bank’s ID number
3 Check digit (error detection)
Checking account number
0134 Customer’s check number
VIN System – Vehicle Identification Number
The manufacturer gives each automobile and truck a unique VIN.
A typical VIN has 17 alphanumeric characters that code information such as country where the vehicle was built, manufacturer, make, body style, engine type, plant where the vehicle was built, model year, model, type of restraint, a check digit, and a production sequence number. 5

6. Chapter 16: Identification Numbers Check Digits
Codabar
An error-detection method used by all major credit-card companies, many libraries, etc.
After the bank issues a card number, it adds an extra digit for error detection created by certain math calculations using a check digit scheme. This makes it difficult to create phony credit cards!
International Standard Book Number (ISBN)
A ten-digit identification number used on books throughout the world that contains a check digit for error detection.
This scheme can detect 100% of single errors and 100% of transposition errors: (Our ISBN may become 13-digits soon, just like Europe.)
A correctly coded ten-digit ISBN a1 a2 …a10 has the property that 10a1 + 9a2 + 8a3 + 7a4 + 6a5 + 5a6 + 4a7 + 3a8 + 2a9 + a10 is evenly divisible by A very detailed check!
Note: ISBN is made up of ten-digits as follows: first digit—published country’s language, next four digits—the publisher, next four digits—type of book, last digit—check digit. 6

7. Chapter 16: Identification Numbers The ZIP Code
Identification numbers sometimes encode geographic data.
In 1963, the U.S. Postal Service numbered every American post office with a five-digit ZIP code—numbers begin with 0 at the points farthest east, and work up to 9 at the points farthest west.
In 1983, the U.S. Postal Service added four digits to the ZIP code, ZIP + 4 code. 7

8. Chapter 16: Identification Numbers Bar Codes
Bar coding is a method for automated data collection.
The identification number is changed into a bar code.
The bar code can be decoded by using a beam of light that is passed over the bars and spaces via a scanning device, such as a hand-held wand or fixed-beam device.
The differences in reflection intensities (black vs. white bars) are detected by the scanner and converted to a string of 0’s and 1’s that represent specific numbers and letters. These strings are called binary coding.
Bar Code – A bar code is a series of dark and light spaces that represent characters.
Binary Code – Any system representing data with only two symbols is a binary code. 8

9. Chapter 16: Identification Numbers Bar Codes
ZIP Code Bar Code
The simplest bar code is the Postnet code used by the U.S. Postal Service and commonly found on business reply forms.
UPC Bar Code
The UPC bar code was first used on grocery items in 1973 and has since spread to most retail products. 9

10. Chapter 16: Identification Numbers Encoding Personal Data
Encoding – Translating data into code.
Coding License Numbers
Some states assign driver’s license numbers with personal data encoded into the number.
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
There is no personal data encoded in the Social Security number
The Social Security numbering scheme predates computers.
The only personal information that can be deduced from the Social Security number is where the holder obtained it. The first three digits show (the state usually) where the applicant applied, with a few exceptions. 10