Confusion about binary expansion of number in $(0,1)$.

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Unfamiliar with discrete mathematics, I wondered in the following two answers Fast way to find period-n points of a tent map?
Techniques for finding period points , why the authors wrote:

1.

"Every real number $x$ in $[0,1]$ can be written (almost) uniquely as $$x=\frac12-\frac12\sum_{n=1}^\infty\frac1{2^n}b_n(x)$$ where, for each $n\geqslant1$, $b_n(x)$ is either $+1$ or $-1$. "

" After a bit of head-scratching, one may get the idea of using a slightly different expansion of every $x$ in $[0,1]$, namely, $$x=\frac12+\frac12\sum_{n\geqslant1}\frac{s_n(x)}{2^n},\qquad s_n(x)\in\{-1,1\}.$$ "

I apologize if the question was previously asked (I also apologize for the title if it does not faithfully reflect the question).

Many thanks for any help with this!