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Section 3.1: Identification Numbers - PowerPoint PPT Presentation


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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

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what is an identification number
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
where have you encountered id numbers
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…
are id numbers random
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?
security features
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
format
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)
security features1
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
checking validity
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
kinds of errors
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?
kinds of errors1
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
how are errors detected
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
how are errors detected1
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
validity vs correctness
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
a sample id number system
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
checking validity1
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
checking correctness
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
detecting errors
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
detecting errors1
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
undetected errors
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!