ThmDex – An index of mathematical definitions, results, and conjectures.
F13540
Formulation 0
Let $r_{N - 1}, \, \ldots, r_1, r_0$ be a D6263: Integer base-2 representation such that
(i) \begin{equation} a = - r_{N - 1} 2^{N - 1} + \sum_{n = 0}^{N - 2} r_n 2^n \end{equation}
Then \begin{equation} - a = 1 - (1 - r_{N - 1}) 2^{N - 1} + \sum_{n = 0}^{N - 2} (1 - r_n) 2^n \end{equation}