Suppose that we send 8-digit numbers (data) plus 2- digit check numbers , total

Question

Suppose that we send 8-digit numbers (data) plus 2-digit check numbers, total of 10-digit numbers over the network. Devise a method of using 2-digit check numbers with which the receiver can check if the first 8 digit numbers were correctly transmitted and received by looking at the last 2-digit check numbers. The method should use the concept of congruence modulo m. Choose the number m so that the likelihood of getting the same 2-digit check number from two different 8-digit numbers is minimal.

PLease i will love it if Show all work so that i can understand it.

Explanation / Answer

Choose m to be a prime number, like 11

Multiply each digit in data with its position and add the result. Take the result mod 11, this will be the checksum digits(if mod 11 = 9, checkdigits will be 09)   

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