MR - Identification Numbers Lesson
Identification Numbers Lesson
Adapted from Course materials (1.A Student Activity Sheet 12&13) for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.
How does a register at the supermarket accurately scan item numbers? Can mistakes in scanning be detected? Identification numbers are present everywhere in society. Today's identification numbers are more sophisticated than those introduced years earlier (for example, Social Security numbers). Today's numbers have a check digit to partially ensure that they have been correctly scanned or entered into a computer.
The check digit is the last number on the bar codes often used in retail for inventory and tracking purposes. The numbers in front of this digit must be composed so that when calculated following the method below, they match the check digit. If the numbers do not match, the bar code number is faulty or incorrect.
The bar code that we encounter most often is the UPC, which was first used on grocery items in 1973 and has since spread to most retail products. UPC codes are 11 digits plus a check digit.
When entering a code number, the single-digit error is most common (for example, keying in 8 instead of 3). Another common error is the transposition error, where the order of two adjacent digits is reversed (for example, writing 83 instead of 38). Systems have been established to detect and correct (when possible) these and other errors almost immediately.
Check your understanding by answering the following questions.
- Suppose you entered 8 instead of 9 when recording the UPC number 1 55210 02149 6. Explain why the UPC method will detect this error.
3(1 + 5 + 1 + 0 + 1 + 8) + 1(5 + 2 + 0 + 2 + 4) = 61
48 + 13 = 61
The check digit number is 6: 61 + 6 = 67
This is an invalid UPC
- When entering UPC numbers, will the error of transposing 2 and 7 be detected? That is, 72 is recorded as 27. How about 2 and 6?
The transposed 2 and 7 will not be detected. The transposed 2 and 6 will be.
Rule - Transposing is not detected if |a - b| = 5
If 2a-2b is a multiple of 10, then a and b can differ by 5.
Credit Cards
All major credit card companies as well as libraries, blood banks, and photofinishing companies use one of the most efficient error detection methods. Codabars consist of 15 digits plus a check digit. How can you determine if a credit card number is valid?
Answer:
( 3 + 2 + 6 + 0 + 9 + 4 + 0 + 1 ) x 2 = 50
2 of these numbers are greater than 4
50 + 2 = 52
(1 + 5+ 0 + 1 + 6 + 3 + 0) = 16
52 + 16 = 68
so the check digit is 2
68 + 2 = 70, a number ending in zero
As we have seen on many television commercials, there are many banking institutions that offer credit cards. The first six digits that appear on a credit card are used for the issue identifier. How many possible issuers are there given each digit 0-9 could be used more than once?
There would be 106 or 1,000,000 possible issue identifiers.
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