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# Error Correction

IP.com Disclosure Number: IPCOM000081801D
Original Publication Date: 1974-Aug-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 1 page(s) / 11K

IBM

## Related People

Bossen, DC: AUTHOR [+2]

## Abstract

An error correction scheme to correct errors in a string of binary coded decimal data digits involves the addition of two check digits C(1) and C(2) to the string of data digits. The check digit C(1) is the remainder obtained by dividing the sum of the digits in the string, by a prime number greater than the total number of digits in the string. Check digit C(2) is the remainder obtained by dividing the sum of each of the digits in the string multiplied by its position in the string, and then divided by the same prime number used to compute C(1).

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Error Correction

An error correction scheme to correct errors in a string of binary coded decimal data digits involves the addition of two check digits C(1) and C(2) to the string of data digits. The check digit C(1) is the remainder obtained by dividing the sum of the digits in the string, by a prime number greater than the total number of digits in the string. Check digit C(2) is the remainder obtained by dividing the sum of each of the digits in the string multiplied by its position in the string, and then divided by the same prime number used to compute C(1).

When the string of data digits is to be checked, two syndrome digits S(1) and S(2) are generated. The syndrome S(1) is generated by subtracting the check digit C(1) from the remainder obtained by dividing the sum of all the digits in the string by the prime number. The syndrome S(2) is generated by subtracting the check digit C(2) from the remainder obtained by taking the sum of all the digits in the string multiplied by their position in the string, and then dividing the sum by the prime number.

If the syndromes S(1) and S(2) are both equal to zero, there is no error in the string of digits. If one of the syndromes in the string is not zero, then there is an error in the check digit C(1) or C(2) which was subtracted from the nonzero syndrome S(1) or S(2). If both syndromes are nonzero, then the ith digit where i is between 1 and 10 is in error. The ith digit is found by multiplying S(2) times the multip...