1 / 20

Section 3.1: Identification Numbers

Math for Liberal Studies. Section 3.1: Identification Numbers. What is an identification number?. An identification number is a sequence of letters and/or numbers that identifies an object, person, place, or concept

zudora
Download Presentation

Section 3.1: Identification Numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math for Liberal Studies Section 3.1: Identification Numbers

  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 type in something random when it asks you for a credit card number? • What should happen?

  5. Security Features • How does the computer know that the number you typed in isn’t valid? • There are some quick ways it might be able to tell • You typed in some letters or symbols instead of all numbers • You didn’t type in 16 digits

  6. Format • ID numbers typically have a common format • Standard PA license plates have a format of three letters followed by four digits • Social security numbers are 9 digits long • Phone numbers are 10 digits long (with area code)

  7. Security Features • What if you type in a number with the correct format? • Should the computer have to look through all the millions of credit card numbers to make sure that what you typed in isn’t on the list? • There are billions of credit cards in the world, even with fast computers this would take too long

  8. 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 an 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

  9. Kinds of Errors • Suppose you call customer service to ask a question about your account • The representative asks for your account number, which is 123456 • What kinds of errors can occur when reporting an ID number like this?

  10. Kinds of Errors • Substitution: 123476 instead of 123456 • This error is the most common, occurring almost 80% of the time • Transposition: 123546 instead of 123456 • This error accounts for around 10% of all errors • Jump transposition: 125436 instead of 123456 • This error is much rarer, accounting for only about 1% of all errors

  11. How Are Errors Detected? • We can immediately see that any of those ID numbers are incorrect, but that’s because we know the real ID number • Put yourself in the position of the company representative on the other end of the phone • That person doesn’t know what the real ID number is, they only know what you tell them

  12. 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

  13. Validity vs. Correctness • When an ID number is communicated, errors can occur, and we can sometimes detect those errors by determining that the erroneous number is invalid • However, sometimes even ID numbers with errors turn out to be valid. In these cases there is no way to know that the ID number is incorrect

  14. A Sample ID Number System • Suppose we run a company that sells phone cards, and each card comes with an account number • The format of the account number is a 6-digit number • Validity is determined using this rule: if the sum of the digits of the account number is 20, then the number is valid. If not, then the number is invalid

  15. Checking Validity • Someone calls in to phone card service and wants to place a call using account number 516224 • We can use our system to determine whether or not this is a valid ID number • 5+1+6+2+2+4 = 20, so this number is valid

  16. Checking Correctness • However, just because the number is valid does not mean that it is correct • It is possible that there was an error that our system didn’t detect

  17. Detecting Errors • Suppose you want to use your account, which has ID number 153182 • However, when you go to type in your number, you accidentally type in 156182 • We can see that an error has occurred because we can see both numbers, but the company only knows the number you typed

  18. Detecting Errors • Is the error detected? • We try our system: 1+5+6+1+8+2 = 23 • Since the sum isn’t 20, we know the ID number 156182 is invalid • We have detected the error

  19. Undetected Errors • This time, suppose you type in your ID number (153182) as 153812 • Again, we can see that an error has occurred, but the question is whether the ID number system can detect the error • In this case, 1+5+3+8+1+2 = 20, which means that the new ID number is valid • The error is not detected!

  20. Valid vs. Correct

More Related