1. Chapter 16: Introduction
MAT 105 Fall 2008
Chapter 16: Introduction

2. What is an identification number?
An identification number is a sequence of letters and/or numbers that identifies an object, person, place, or concept
The number should unambiguously identify something: no two things should have the same ID number

3. Where have you encountered ID numbers?
Think about the different ways you encounter ID numbers in your daily life…
License plate
Driver’s license number
Student ID number
Social Security number
Phone numbers
Credit card numbers
ISBN (International Standard Book Number)
UPC (Universal Product Code)
Many, many more…

4. Are ID numbers random?
What happens if you go to Amazon.com and try to order something with a random credit card number?
What should happen?

5. Security Features
How does the computer know that the number you typed in isn’t valid?
Should the computer have to look through all the millions of credit card numbers to make sure that the one you made up isn’t on the list?

6. Checking Validity
Most ID numbers have a quick way to check to make sure that the number is valid
This is not just for security, but to detect errors
If the ID number is entered incorrectly, it is important that the error is caught; you don’t want your account to get charged for someone else’s order

7. Kinds of Errors Substitution: 123476 instead of 123456
This error is the most common, occurring almost 80% of the time
Transposition: instead of
This error accounts for around 10% of all errors
Jump transposition: instead of
This error is much rarer, accounting for only about 1% of all errors

8. How Are Errors Detected?
Most errors are detected using check digits
Check digits are extra digits attached to the ID number that are only used for checking that the ID number is valid
Many different check digit systems are used, and we will study several of them
Some check digit systems are secret so that they cannot be used to generate fake (but valid) ID numbers