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# Self-Checking Numbering System

IP.com Disclosure Number: IPCOM000098331D
Original Publication Date: 1960-Aug-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 2 page(s) / 19K

IBM

## Related People

Davis, RA: AUTHOR

## Abstract

A key or check digit is appended to an existing number to prevent the number from being altered by incorrect or transposed digits in subsequent operations. The key digit is selected so that upon cross addition of weighted multiples of all the digits of the number and subtraction of the key digit, in accordance with a rule of differential multiplication, the result, with elevens cast out, will be zero.

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Self-Checking Numbering System

A key or check digit is appended to an existing number to prevent the number from being altered by incorrect or transposed digits in subsequent operations. The key digit is selected so that upon cross addition of weighted multiples of all the digits of the number and subtraction of the key digit, in accordance with a rule of differential multiplication, the result, with elevens cast out, will be zero.

The check digit is created as the numerator of the fractional remainder as illustrated for a six digit number A B C D E F. (7A+6B+5C+4D+3E+2F)/11

Thus, for a base number 127485, the check digit 5, the numerator of the fractional remainder, is derived as follows: ( (7x1) + (6x2) + (5x7)+ (4x4) + (3x8) + (2x5) )=104/11=9 5/11

The check digit is appended to the base number to create a selfchecking number 1274855.

The check digit is the difference between the sum of the products and the next lower number divisible by 11. Therefore, by selecting the base 11, the check digit may be determined merely by finding the sum of the products of the units position in the above equation and dropping any carry.

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