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?

  • $\begingroup$ 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)? $\endgroup$ – user491874 Dec 30 '17 at 19:41
  • $\begingroup$ It is not at all clear what you want to do. $\endgroup$ – copper.hat Dec 30 '17 at 20:37

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