US Postal Money Orders

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. 

Definition 2.4.1. Let aia2a3a4a5a6Ar Z8Uaaio the ten-digit document number associated with a US postal tnoney order. The check digit uu, which is appended to this number to create the ll-digit identification number 010303 4 isuearogagaioai 1. is determined by 

Consider the identification number 67021200988 which describes a document numbered aia2aza4asas(i7agOgaio = 6702120098. The check digit Ou = 8, since 

Consider another possible money order number, 31059112852. If this is to be a valid number, the remainder when 3 + H-0-f-5-l-9+l + l + 2- -8 + 5is divided by 9 must be equal to the check digit of 2. However, 

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US Postal Money Order with Identification Number 67021200988... 

The US postal money order number 67021200988 in Figure 1.2 has length n = 11. 

US postal money order identification numbers always consist of 11 digits and are denoted 010203040500070809010011. For the number 67021200988,... 

So. why does this scheme not catch the types of single-digit errors mentioned above Consider the following case, where a 9, in any position except the check digit position, is replaced by a 0 in an arbitrary US postal money order identification number. 

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. 

Explain why the US postal money order check digit schenoe catches only transposition-of-adjacent-digits errors that involve the check digit. (HINT Try a few examples and look at the sum of the digits.)... 

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