how I love programming nerd conversations!
I take that as a compliment, we didn't help solve your problem but still made you happy
(Or are you a textwriter looking for inspiration for some sitcom? 
Back to your original question
Let me rephrase: "Is there an algebraic equation to convert between base10 and binary?"
It is still not clear what you want, Please give an example how such an algebraic equation looks like, and where the base 10 and binary fits in....
There are 10 types of people in this world those that know binary and those that don't.