Is there any Maclaurin series for decimal to binary conversion with binary being n-bits?

So I am doing a research about binary operations and I really want to relate it with series and sumatories.

First I wanted get a function to convert decimal to binary and later on get the Maclaurin series so it is not restricted to 8 bit.

Starting with the 8 bit, the first thing I´ve came up with is this: $$10^8*0^{(-1)^{f(X)}}+10^7*0^{(-1)^{f(X)}}+10^6*0^{(-1)^{f(X)}}+10^5*0^{(-1)^{f(X)}}+10^4*0^{(-1)^{f(X)}}+10^3*0^{(-1)^{f(X)}}+10^2*0^{(-1)^{f(X)}}+10^1*0^{(-1)^{f(X)}}$$ Being $f(x)= g(x) * n - x$ ; where n is a number such as 128, 64, 32, 16, 8, 2, 1; and x the number to convert. I want $f(x)$ to be even/odd when $n - x$ is negative or positive.

Is that possible?

• Whatever is $g(x)$? What does $0^{-1}$ mean (can $f(X)$ may be odd; I assume yes, or you wouldn't bother writing it)? – user491874 Dec 30 '17 at 19:41
• It is not at all clear what you want to do. – copper.hat Dec 30 '17 at 20:37