Question 2.10: Add 010011112 to 001000112 using signed-magnitude arithmetic...
Add 01001111_{2} to 00100011_{2} using signed-magnitude arithmetic.
\begin{matrix} \\ 0 \\ 0& \\ 0 \end{matrix} \begin{matrix} \\ \\ + \\ \end{matrix} \begin{array}{r c} \begin{matrix} \\ 1 \\ 0 \end{matrix} & \begin{matrix}\\ 0 \\ 1 \end{matrix} & \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 \\ 1 \end{matrix}& \begin{matrix}\\ 1\\ 1 \end{matrix}&\\ \hline \begin{matrix} 1\end{matrix}&\begin{matrix} 1\end{matrix} &\begin{matrix}1\end{matrix}&\begin{matrix}0\end{matrix}&\begin{matrix}0\end{matrix} &\begin{matrix}1\end{matrix}&\begin{matrix}0\end{matrix}\end{array} \begin{array}{r c} \begin{matrix}\Leftarrow \text{carries} \\ (79)\\+(35)\\ \hline \begin{matrix}(114)\end{matrix}\end{matrix}\end{array}
The arithmetic proceeds just as in decimal addition, including the carries, until we get to the seventh bit from the right. If there is a carry here, we say that we have an overflow condition and the carry is discarded, resulting in an incorrect sum. There is no overflow in this example.
We find 01001111_{2}+00100011_{2}=01110010_{2} in signed-magnitude representation.
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