Question 2.22: Find the sum of 12610 and 810 in binary using two’s compleme...
Find the sum of 126_{10} and 8_{10} in binary using two’s complement arithmetic.
\begin{matrix} \text{Discard last} \\ \text{carry}. \\ \end{matrix} \begin{matrix} 0\\ \\ \\ \end{matrix}\begin{matrix} \leftarrow \\ \\ + \end{matrix} \begin{array}{r c} \begin{matrix} \\ 1 \\ 0 \\ 0\end{matrix} & \begin{matrix}\\ 1 \\ 1 \\ 0\end{matrix} & \begin{matrix}\\ 1 \\ 1 \\ 0\end{matrix}& \begin{matrix}\\ 1 \\ 1 \\ 0\end{matrix} &\begin{matrix}\\ \\ 1 \\ 1\end{matrix}& \begin{matrix}\\ \\ 1 \\ 0\end{matrix}& \begin{matrix}\\ \\ 1 \\ 0\end{matrix}&\begin{matrix}\\ \\ 0 \\ 0\end{matrix}& \\ \hline \begin{matrix} 1\end{matrix}&\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}\end{array} \begin{array}{r c} \begin{matrix}\\ \Leftarrow \text{carries} \\ (126)\\+(8)\\ \hline \begin{matrix}(-122???)\end{matrix}\end{matrix}\end{array}
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