Chapter 16: Identification Numbers
Lesson Plan
For All Practical
Purposes
Mathematical Literacy in
Today’s World, 9th ed.
 Check Digits
 The ZIP Code
 Bar Codes
 Encoding Personal Data
© 2013 W. H. Freeman and Company
Chapter 16: Identification Numbers
Identification Numbers
 Identification Numbers
 Modern identification numbers
serve at least two functions:
1. The number should
unambiguously identify the
person or thing with which it
is associated .
2. 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.
Chapter 16: Identification Numbers
Check Digits
 Check Digit
 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
6302438384 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.
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 0 38000 00127 7 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.
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)
22 633 78 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.
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: (Note: Our books also have a 13-digit ISBN )
 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 11. 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.
Chapter 16: Identification Numbers
The ZIP Code
 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.
Chapter 16: Identification Numbers
Bar Codes
 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 bars and
light spaces that represent
characters.
Binary Code – Any system
representing data with only
two symbols is a binary
code.
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.
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.