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?