| (i) | $r_0, r_1, \ldots, r_{N - 1} \in \{ 0, 1 \}$ are each a D1043: Boolean number |
| (i) | $r_0, r_1, \ldots, r_{N - 1} \in \{ 0, 1 \}$ are each a D1043: Boolean number |
| ▶ | D6269: N-bit integer |
| ▶ | R5720: Negative of base-2 integer iff bits negated plus one |
| ▶ |
Example 0
In the case of $N = 4$, 1111 is a base-2 representation of -1 because we have
\begin{equation}
\begin{split}
-2^3 + 2^2 + 2^1 + 2^0
= -8 + 4 + 2 + 1
= -1
\end{split}
\end{equation}
Flipping the highest-order bit, 0111 is a base-2 representation of 7 because we have
\begin{equation}
\begin{split}
2^2 + 2^1 + 2^0
= 4 + 2 + 1
= 7
\end{split}
\end{equation}
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