Find the sum of 12610 and 810 in binary using two’s complement arithmetic.

Question

Find the sum of [latex]126_{10}[/latex] and [latex]8_{10}[/latex] in binary using two’s complement arithmetic.

Accepted Answer

[latex]\begin{matrix} ext{Discard last} \ ext{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 ext{carries} \ (126)\+(8)\ \hline \begin{matrix}(-122???)\end{matrix}\end{matrix}\end{array}[/latex]

Question 2.22: Find the sum of 12610 and 810 in binary using two’s compleme...

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