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For some cases, modulo 2 binary division is giving the same remainder as a base 10 modulus but for some cases it is not. Is there some relationship between the two remainders? Example:- 

1.) q = 101000110100000
p = 110101
modulo 2 binary division remainder = 01110
and  In base 10,
q = 20896
p = 53
and q%p = 14 which is the same as 01110

2.) q = 11001001000
p = 1001
modulo 2 binary division remainder is 011
and In base 10,
q = 1608
p = 9
and q%p = 6 which is different from 011.

So is there some relationship or it is totally unrelated? I want to know if I can derive base 2 modulo division remainder by doing decimal modulus.

Krash
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1 Answers1

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No. There is no relationship. A polynomial over GF(2) can be represented as a string of bits. An integer can be represented as a string of bits. There the similarity ends. They are two entirely different beasts.

And there is no inherent "base 10" or "decimal" here, except in displaying the numbers. You are comparing integer modulo with polynomial modulo. The integers don't care what base you display them in.

Mark Adler
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