<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[12pt]{article}

\usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox}

\usepackage{arydshln}

\parskip = .2in
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\pagestyle{empty}

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\begin{document}



X = 0.1011 0111 10 (734/1024)

S = 0.1101 1000 11\ 00 (3468/4096), negative sticky bit
{\small
\begin{center}
\begin{tabular}{ccccc}
            &amp;$X             $&amp;$         0000.1011\ 0111\ 1000   $&amp;          &amp;$S_0={\color{blue}0001}.0000\ 0000\ 0000$\\
            &amp;$WS_0=4(X-1)   $&amp;$         1110.1101\ 1110\ 0000   $&amp;          &amp;$SM_0={\color{blue}0000}.0000\ 0000\ 0000\phantom{M}$\\
            &amp;$WC_0          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;$K_0=0001.0000\ 0000\ 0000\ $\\
            &amp;                &amp;                                   &amp;          &amp;$C_0=1111.0000\ 0000\ 0000\,$\\
    \hdashline\\
    Step 1: &amp;$WS_0          $&amp;$         1110.1101\ 1110\ 0000   $&amp;          &amp;\\
            &amp;$WC_0          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110.110\ \text{so}\ s_1=-1$)\\
            &amp;$F_1=2S_0-K_1$&amp;${\color{blue}0001.11}00\ 0000\ 0000$&amp;          &amp;$S_1={\color{blue}0000.11}00\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_1={\color{blue}0000.10}00\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0001\ 1110\ 0000   $&amp;$\ll2    $&amp;$K_1=0000.0100\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         0001.1000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_1=1111.1100\ 0000\ 0000\,$\\
    \hdashline\\    
    Step 2: &amp;$WS_1          $&amp;$         1100.0111\ 1000\ 0000   $&amp;          &amp;\\
            &amp;$WC_1          $&amp;$         0110.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0010.011\ \text{so}\ s_2=2$)\\
            &amp;$F_2=-4S_1-4K_2$&amp;${\color{blue}1100.1100}\ 0000\ 0000$&amp;        &amp;$S_2={\color{blue}0000.1110}\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_2={\color{blue}0000.1101}\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         0110.1011\ 1000\ 0000   $&amp;$\ll2    $&amp;$K_2=0000.0001\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         1000.1000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_2=1111.1111\ 0000\ 0000\,$\\
    \hdashline\\
    Step 3: &amp;$WS_2          $&amp;$         1010.1110\ 0000\ 0000   $&amp;          &amp;\\
            &amp;$WC_2          $&amp;$         0010.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1100.111\ \text{so}\ s_3=-2$)\\
            &amp;$F_3=4S_2-4K_3$&amp;${\color{blue}0011.0111\ 00}00\ 0000$&amp;         &amp;$S_3={\color{blue}0000.1101\ 10}00\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_3={\color{blue}0000.1101\ 01}00\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1011.1001\ 0000\ 0000   $&amp;$\ll2    $&amp;$K_3=0000.0000\ 0100\ 0000\ $\\
            &amp;$carry         $&amp;$         0100.1100\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_3=1111.1111\ 1100\ 0000\,$\\
    \hdashline\\
    Step 4: &amp;$WS_3          $&amp;$         1110.0100\ 0000\ 0000   $&amp;          &amp;\\
            &amp;$WC_3          $&amp;$         0011.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0001.010\ \text{so}\ s_4=1$)\\
            &amp;$F_4=-2S_3-K_4$&amp;${\color{blue}1110.0100\ 1111}\ 0000$&amp;        &amp;$S_4={\color{blue}0000.1101\ 1001}\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_4={\color{blue}0000.1101\ 1000}\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         0011.0000\ 1111\ 0000   $&amp;$\ll2    $&amp;$K_4=0000.0000\ 0001\ 0000\ $\\
            &amp;$carry         $&amp;$         1100.1000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_4=1111.1111\ 1111\ 0000\,$\\
    \hdashline\\
    Step 5: &amp;$WS_4          $&amp;$         1100.0011\ 1100\ 0000   $&amp;          &amp;\\
            &amp;$WC_4          $&amp;$         0010.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110.001\ \text{so}\ s_5=-1$)\\
            &amp;$F_5=2S_4-K_5 $&amp;${\color{blue}0001.1011\ 0001\ 11}00$&amp;        &amp;$S_5={\color{blue}0000.1101\ 1000\ 11}00$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_5={\color{blue}0000.1101\ 1000\ 10}00\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.1000\ 1101\ 1100   $&amp;$\ll2    $&amp;$K_5=0000.0000\ 0000\ 0100\ $\\
            &amp;$carry         $&amp;$         0000.0110\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_5=1111.1111\ 1111\ 1100\,$\\
    \hdashline\\
    Step 6: &amp;$WS_5          $&amp;$         1110.0011\ 0111\ 0000   $&amp;          &amp;\\
            &amp;$WC_5          $&amp;$         0001.1000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1111.101\ \text{so}\ s_6=0$)\\
            &amp;$F_6=0        $&amp;${\color{blue}0000.0000\ 0000\ 0000}$&amp;         &amp;$S_6={\color{blue}0000.1101\ 1000\ 1100}$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_6={\color{blue}0000.1101\ 1000\ 1011}\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.1011\ 0111\ 0111   $&amp;$\ll2    $&amp;$K_6=0000.0000\ 0000\ 0001\ $\\
            &amp;$carry         $&amp;$         0000.0000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_6=1111.1111\ 1111\ 1111\,$\\
    \hdashline\\
    Terminate&amp;Square Root&amp;0000.11 01\ 10 00\ 10 (11)
\end{tabular}
\end{center}
}

X = 0.1001\ 0101\ 00 (596/1024)

S = 0.1100 0011 01\ 01 (3125/4096)
{\small
\begin{center}
\begin{tabular}{ccccc}
            &amp;$X             $&amp;$         0000.1001\ 0101\ 0000   $&amp;          &amp;$S_0={\color{blue}0001}.0000\ 0000\ 0000$\\
            &amp;$WS_0=4(X-1)   $&amp;$         1110.0101\ 0100\ 0000   $&amp;          &amp;$SM_0={\color{blue}0000}.0000\ 0000\ 0000\phantom{M}$\\
            &amp;$WC_0          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;$K_0=0001.0000\ 0000\ 0000\ $\\
            &amp;                &amp;                                   &amp;          &amp;$C_0=1111.0000\ 0000\ 0000\,$\\
    \hdashline\\
    Step 1: &amp;$WS_0          $&amp;$         1110.0101\ 0100\ 0000   $&amp;          &amp;\\
            &amp;$WC_0          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110.010\ \text{so}\ s_1=-1$)\\
            &amp;$F_1=2S_0-K_1  $&amp;${\color{blue}0001.11}00\ 0000\ 0000$&amp;        &amp;$S_1={\color{blue}0000.11}00\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_1={\color{blue}0000.10}00\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.1001\ 0100\ 0000   $&amp;$\ll2    $&amp;$K_1=0000.0100\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         0000.1000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_1=1111.1100\ 0000\ 0000\,$\\
    \hdashline\\    
    Step 2: &amp;$WS_1          $&amp;$         1110.0101\ 0000\ 0000   $&amp;          &amp;\\
            &amp;$WC_2          $&amp;$         0010.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0000.010\ \text{so}\ s_2=0$)\\
            &amp;$F_2=0       $&amp;${\color{blue}0000.0000}\ 0000\ 0000$&amp;          &amp;$S_2={\color{blue}0000.1100}\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_2={\color{blue}0000.1110}\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1100.0101\ 0000\ 0000   $&amp;$\ll2    $&amp;$K_2=0000.0001\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         0100.0000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_2=1111.1111\ 0000\ 0000\,$\\
    \hdashline\\
    Step 3: &amp;$WS_2          $&amp;$         0001.0100\ 0000\ 0000   $&amp;          &amp;\\
            &amp;$WC_2          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0001.010\ \text{so}\ s_3=1$)\\
            &amp;$F_3=-2S_2-K_3$&amp;${\color{blue}1110.0111\ 11}00\ 0000$&amp;         &amp;$S_3={\color{blue}0000.1100\ 01}00\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_3={\color{blue}0000.1100\ 00}00\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0011\ 1100\ 0000   $&amp;$\ll2    $&amp;$K_3=0000.0000\ 0100\ 0000\ $\\
            &amp;$carry         $&amp;$         1000.1000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_3=1111.1111\ 1100\ 0000\,$\\
    \hdashline\\
    Step 4: &amp;$WS_3          $&amp;$         1100.1111\ 0000\ 0000   $&amp;          &amp;\\
            &amp;$WC_3          $&amp;$         0010.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110.111\ \text{so}\ s_4=-1$)\\
            &amp;$F_4=2S_3-K_3  $&amp;${\color{blue}0001.1000\ 0111}\ 0000$&amp;        &amp;$S_4={\color{blue}0000.1100\ 0011}\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_4={\color{blue}0000.1100\ 0010}\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0111\ 0111\ 0000   $&amp;$\ll2    $&amp;$K_4=0000.0000\ 0001\ 0000\ $\\
            &amp;$carry         $&amp;$         0001.0000\ 0000\ 0000   $&amp;$\ll2    $&amp;$C_4=1111.1111\ 1111\ 0000\,$\\
    \hdashline\\
    Step 5: &amp;$WS_4          $&amp;$         1101.1101\ 1100\ 0000   $&amp;          &amp;\\
            &amp;$WC_4          $&amp;$         0100.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0001.110\ \text{so}\ s_5=1$)\\
            &amp;$F_5=-2S_4-K_4 $&amp;${\color{blue}1110.0111\ 1001\ 11}00$&amp;        &amp;$S_5={\color{blue}0000.1100\ 0011\ 01}00$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_5={\color{blue}0000.1100\ 0011\ 00}00\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         0111.1010\ 0101\ 1100   $&amp;$\ll1    $&amp;$K_5=0000.0000\ 0000\ 0100\ $\\
            &amp;$carry         $&amp;$         1000.1011\ 0000\ 0000   $&amp;$\ll1    $&amp;$C_5=1111.1111\ 1111\ 1100\,$\\
    \hdashline\\
    Step 6: &amp;$WS_5          $&amp;$         1110.1001\ 0111\ 0000   $&amp;          &amp;\\
            &amp;$WC_5          $&amp;$         0010.1100\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0001.010\ \text{so}\ s_6=1$)\\
            &amp;$F_6=          $&amp;$                                 $&amp;          &amp;$S_5={\color{blue}0000.1100\ 0011\ 0101}$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_5={\color{blue}0000.1100\ 0011\ 0100}\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         0001.1110\ 1001\ 0111   $&amp;$\ll1    $&amp;$K_5=0000.0000\ 0000\ 0001\ $\\
            &amp;$carry         $&amp;$         1110.0010\ 1100\ 0000   $&amp;$\ll1    $&amp;$C_5=1111.1111\ 1111\ 1111\,$\\
    \hdashline\\
    Terminate
\end{tabular}
\end{center}
}

\end{document}
</pre></body></html>