ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
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Set of natural numbers
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Integer
Definition D6263
Integer base-2 representation
Formulation 0
Let $N \in \{ 1, 2, 3, \ldots \}$ be a D5094: Positive integer such that
(i) $r_0, r_1, \ldots, r_{N - 1} \in \{ 0, 1 \}$ are each a D1043: Boolean number
Then $ r_{N - 1}, \ldots, r_1, r_0$ is a base-2 representation in $N$ bits for $a \in \mathbb{Z}$ if and only if \begin{equation} a = - r_{N - 1} 2^{N - 1} + \sum_{n = 0}^{N - 2} r_n 2^n \end{equation}
Children
D6269: N-bit integer