What kind of 'calculations' do you mean? All programming languages do mod arithmetic. Mod 2 arithmetic is very easy - there are only 2 elements in the field. Why would you need any help with that? You can also do any calculations as integers, and then reduce mod 2.
If you really want free software, then GAP and PARI (I think that's free) will do interesting things over finite fields.
well, my problem is,when calculating eigenvalues of a mod 2 (only 1 and 0) matrix, I'm getting decimals. I'm not sure how to convert decimals to mod 2.
Then you're doing something wrong, like using the wrong methods in the wrong place. There is no meaningful sense in which decimals are related to mod 2 results. And as I've explained elsewhere, the only roots mod 2 are 0 and 1 so this is a trivial check.