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# Check Digit Schemes Essay

1126 words - 5 pages

In an age when information is increasingly transmitted through electronic formats, maintaining the accuracy of information is crucial. Whether this information is as simple as a book loaned by a library or as important as a banking account number, maintaining consistency during information transmission is critical to preventing monetary or organizational errors. To maintain consistency in various information transfers, check digit schemes based on number theory are used to dectect when errors occur. This paper will examine the value of check digit schemes in light of their application and mathematics.
To begin with, a basic understanding of check digit schemes reveals the value of this number theory application. Check digit schemes exist in almost every identification number. The authors Pommersheim, Marks, and Flapan (2010) noted that common examples of check digit schemes exist in ISBN numbers, airline tickets, money orders, and barcodes on retail items. From these examples, it is clear that check digit schemes are a common application of number theory that quietly impacts everyday life. This impact is found in the function of check digit schemes. In summarizing this function, mathematics professor Joseph Kirtland (2001) noted that “Most check digit schemes append an extra digit or digits, called the check digit(s), to the identification number and then use the digit(s) to check to check for errors after the number has been transmitted” (p. 5). From the author’s overview, the impact of check digit schemes is found in the prevention of errors that accompany their usage. By implementing a check digit scheme in a computer or scanner, the device can quickly check the validity of an identification number and report or correct the number to insure proper transmission. When discussing the validation process, it is important it know what kinds of errors are detected by check digit schemes. Errors vary in type and complexity, but Kirtland (2001) noted that check digit schemes attempt to detect errors that involve one digit being altered (a single-digit error) or two adjacent numbers being switched in order (a transposition error). This detection seems trivial until one considers the work of Pommsheim, Marks, and Flapan (2010), who noted that “Single-digit errors and transposition errors… account for 90% of all identification number transmission errors” (p, 267). Essentially, schemes detect a majority of transmission errors. By applying check digit schemes, information is accurately transferred between computers and other electronic devices. Overall, the usage of check digit schemes is essential for accurate electronic data transfer.
Along with usage, an overview of the mathematics of check digit schemes demonstrates the value of the application. As previously outlined, check digit schemes use a check digit to detect errors in a data transmission. This detection is based on modular arithmetic, a topic from number theory. In...

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