An D995: Integer $a \in \mathbb{Z}$ is a 32-bit integer if and only if \begin{equation} \exists \, r_0, r_1, \ldots, r_{31} \in \{ 0, 1 \} : a = - r_{31} 2^{31} + \sum_{n = 0}^{30} r_n 2^n \end{equation}