Question

subatract the number (85) from (113) using 2's complement method​

Answer 1

$\textbf{Question}$

   $\textsf{ (113)_{10} \:\: - \:\: (85)_{10} \: using the 2's complement.}$

$\textbf{Answer}$

    $\textsf{First converting the numbers into their binary equivalent,}\\\textsf{\hspace{1.5em} (85)_{10} = (1010101)_2 \: and,}\\\textsf{\hspace{1.5em} (113)_{10} = (1110001)_2 }$

    $\textsf{Taking the 2's complement of (1010101)_2 }\\\textsf{\hspace{1.5em} 1010101 \rightarrow 0101010 \rightarrow \boxed{0101011}\:.}$

    $\textsf{Adding the the numbers to obtain the result,}$

          $\textbf{\hspace{2.9em} \footnotesize{1 \hspace{3.1em} 1 \: 1}}\\\textsf{\hspace{2em} 1 \: 1 \: 1 \: 0 \: 0 \: 0 \: 1}\\\textsf{\hspace{.35em} + \: 0 \: 1 \: 0 \: 1 \: 0 \: 1 \: 1}\\\rule{11.2em}{0.05em}\\\textsf{\hspace{.3em}\boxed{1} \: 0 \: 0 \: \underline{1 \: 1 \: 1 \: 0 \: 0}}$

    $\textsf{Hence, (113)_{10} - (85)_{10} = (28)_{10} \: or (11100)_2 }$