ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Empty map
▼ Collection
▼ Ring element collection
▼ Ring element combination
▼ Basic natural number basis representation
Definition D5428
Natural number base-2 representation
Formulation 2
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 $a \in \mathbb{N}$ if and only if \begin{equation} a = \sum_{n = 0}^{N - 1} r_n 2^n \end{equation}