Check digit scheme

Most check digit schemes append an extra digit or digits, called the check digitfsh to the identification number and then use the digitfs) to check for errors after the number has been transmitted. To illustrate one possible method, consider the following scenario ... 

Different identification number systems use different check digit schemes. Some are more effective than others. Given that single-digit errors and transposition-of-adjacent-digits errors account for almost 90% of all errors (see Table 1.2), any scheme that is developed should at the very least catch these two types of errors. Some of the simpler schemes, while better than nothing, do not even do this. 

Of course, the more errors a scheme catches, the more complicated it will be. There are more advanced check digit schemes that catch all of the errors mentioned in Table 1.2. The main goal of this book is to develop the mathematics necessary to understand a variety of check digit schemes, examine their applications, and evaluate just how well they actually work. 

You are in charge of all the computer equipment on the Marist College campus. To help keep track of all the equipment, you decide to develop an identification number system. To avoid transmission errors, this system will also incorporate a check digit scheme. 

Develop a check digit scheme for this number system. In other words, you must develop the process that creates the check digit a. There is no wrong answer as long as the method is mathematically sound. Give some examples of how it works. For example, if 27561 is a CN, what would the check digit be ... 

Most check digit schemes place the check digit as the last digit in the number. Is there a mathematical reason or other reason for this Explain your answer. 

Summarizing, Write a short essay that will explain to someone not familiar with check digit schemes the motivation behind the creation of check digit schemes. Clearly specify the relationship between check digit schemes and identification numbers. 

Developmental Assignment Argumentation. Find an identification number system that, as far as you know, does not contain a check digit scheme. Make a case for the creation of a new identification number system that incorporates a check digit scheme. That is, give reasons why such a system/scheme might be useful and for whom. 

Number Theory, Check Digit Schemes, and Cryptography... 

This chapter begins with an investigation of integer division and modulo arithmetic. We then explore check digit schemes that employ the number theoretic concepts we have developed. The chapter ends with an application of these concepts to cryptography. 

Recall the four operations from arithmetic addition, subtraction, multiplication, and division. These operations, along with integers and whole numbers, will form the basis of our investigation into check digit schemes. 

Developmental Assignment Combine the summary of sections 1 and 2 of this chapter with the summary written for section 3. The concepts and terms introduced in sections 1 and 2 are needed in section 3. All of these concepts will be central to the study of cryptography and check digit schemes. 

The next four sections of this chapter wilt study the application of these number theoretic ideas to four different check digit schemes. While the first two schemes (US postal money orders and airline ticket numbers) are fairly simple, they do not fare well with regards to catching all of the types of errors listed in Table 1.2. The last two schemes (UPC and ISBN) are nnore sophisticated and do a better job in catching errors. 

The US Post Office uses a mod 9 check digit scheme (3], (7]. The check digit is the remainder when the sum of digits in the document number is divided by 9. 

Recall that the goal for any check digit scheme is to catch all the errors listed in Table 1.2. At the very least, a scheme should catch all the single-digit and transposition-of-adjacent-digits errors. Consider the valid money order identification number that was just created. Listed below are two different single-digit errors. 

The following two numbers are claimed to be US postal money order identification numbers. Using the US postal money order check digit scheme, determine which is a valid number and which is invalid. 

The number 3980062110 is to be used to identify a US postal money order. Using the US postal money check digit scheme, assign a check digit to this identification number. Be sure to identify the check digit and then to write out the entire document number. 

At the end of this section, it was mentioned that the US postal money order check digit scheme catches transposition-of-adjacent-digits errors only when they involve the check digit. The goal of this activity is to determine why. 

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