Question 2.17: Add 2310 to −910 using one’s complement arithmetic.
Add 23_{10} to −9_{10} using one’s complement arithmetic.
\begin{matrix} \text{The last carry is added} \\ \text{to the sum} \end{matrix} \begin{matrix}1 \leftarrow \\ \\ + \\ \\ \\ \\ \end{matrix} \begin{array}{r c} \begin{matrix} 1 \\ 0 \\ 1 \end{matrix} & \begin{matrix}1 \\ 0 \\ 1 \end{matrix} & \begin{matrix}1 \\ 0 \\ 1 \end{matrix}& \begin{matrix}\\ 1 \\1 \end{matrix}&\begin{matrix}1\\0 \\0 \end{matrix}& \begin{matrix}1\\ 1 \\ 1 \end{matrix}& \begin{matrix}\\ 1\\ 1 \end{matrix} & \begin{matrix} \\ 1 \\ 0 \end{matrix}&\\ \hline \begin{matrix} 0\end{matrix}&\begin{matrix} 0\end{matrix} &\begin{matrix}0\end{matrix} &\begin{matrix}0\end{matrix}&\begin{matrix}1\end{matrix} &\begin{matrix}1\end{matrix}&\begin{matrix}0\end{matrix} & \begin{matrix}1\end{matrix}\\ & & & & & & + & 1 \\ \hline 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \end{array} \begin{array}{r c} \begin{matrix}\Leftarrow \text{carries} \\ (23)\\+(- 9)\\ \hline \\ \\ \begin{matrix}14_{10} \end{matrix}\end{matrix}\end{array}
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