<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
\parindent  = 0in

\pagestyle{empty}

%==========
%==========

\begin{document}

X = 0.0111 0011 1001 (1849/4096)

S = 0.1010 1100 0000 (2752/4096)
{\small
\begin{center}
\begin{tabular}{ccccc}
            &amp;$X             $&amp;$         0000.0111\ 0011\ 1001   $&amp;          &amp;$S_0={\color{blue}0001}.0000\ 0000\ 0000$\\
            &amp;$WS_0=2(X-1)   $&amp;$         1110.1110\ 0111\ 0010   $&amp;          &amp;$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          $&amp;$         1110.1110\ 0111\ 0010   $&amp;          &amp;\\
            &amp;$WC_0          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110\ \text{so}\ s_1=-1$)\\
            &amp;$F_1=2S_0-K_1 $&amp;${\color{blue}0001.1}000\ 0000\ 0000$&amp;          &amp;$S_1={\color{blue}0000.1}000\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_1={\color{blue}0000.0}000\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0110\ 0111\ 0010   $&amp;$\ll1    $&amp;$K_1=0000.1000\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         0001.0000\ 0000\ 0000   $&amp;$\ll1    $&amp;$C_1=1111.1000\ 0000\ 0000\,$\\
    \hdashline\\    
    Step 2: &amp;$WS_1          $&amp;$         1110.1100\ 1110\ 0100   $&amp;          &amp;\\
            &amp;$WC_1          $&amp;$         0010.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0000\ \text{so}\ s_2=1$)\\
            &amp;$F_2=-2S_1-K_2$&amp;${\color{blue}1110.11}00\ 0000\ 0000$&amp;          &amp;$S_2={\color{blue}0000.11}00\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_2={\color{blue}0000.10}00\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         0010.0000\ 1110\ 0100   $&amp;$\ll1    $&amp;$K_2=0000.0100\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         1101.1000\ 0000\ 0000   $&amp;$\ll1    $&amp;$C_2=1111.1100\ 0000\ 0000\,$\\
    \hdashline\\
    Step 3: &amp;$WS_2          $&amp;$         0100.0001\ 1100\ 1000   $&amp;          &amp;\\
            &amp;$WC_2          $&amp;$         1011.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1111\ \text{so}\ s_3=0$)\\
            &amp;$F_3=0       $&amp;${\color{blue}0000.000}0\ 0000\ 0000$&amp;          &amp;$S_3={\color{blue}0000.110}0\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_3={\color{blue}0000.101}0\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0001\ 1100\ 1000   $&amp;$\ll1    $&amp;$K_3=0000.0010\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         0000.0000\ 0000\ 0000   $&amp;$\ll1    $&amp;$C_3=1111.1110\ 0000\ 0000\,$\\
    \hdashline\\
    Step 4: &amp;$WS_3          $&amp;$         1110.0011\ 1001\ 0000   $&amp;          &amp;\\
            &amp;$WC_3          $&amp;$         0000.0000\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110\ \text{so}\ s_4=-1$)\\
            &amp;$F_4=2S_3-K_4 $&amp;${\color{blue}0001.0111}\ 0000\ 0000$&amp;          &amp;$S_4={\color{blue}0000.1011}\ 0000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_4={\color{blue}0000.1010}\ 0000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0100\ 1001\ 0000   $&amp;$\ll1    $&amp;$K_4=0000.0001\ 0000\ 0000\ $\\
            &amp;$carry         $&amp;$         0000.0110\ 0000\ 0000   $&amp;$\ll1    $&amp;$C_4=1111.1111\ 0000\ 0000\,$\\
    \hdashline\\
    Step 5: &amp;$WS_4          $&amp;$         1110.1001\ 0010\ 0000   $&amp;          &amp;\\
            &amp;$WC_4          $&amp;$         0000.1100\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=1110\ \text{so}\ s_5=-1$)\\
            &amp;$F_5=2S_4-K_5 $&amp;${\color{blue}0001.0101\ 1}000\ 0000$&amp;          &amp;$S_5={\color{blue}0000.1010\ 1}000\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_5={\color{blue}0000.1010\ 0}000\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         1111.0000\ 1010\ 0000   $&amp;$\ll1    $&amp;$K_5=0000.0000\ 1000\ 0000\ $\\
            &amp;$carry         $&amp;$         0001.1010\ 0000\ 0000   $&amp;$\ll1    $&amp;$C_5=1111.1111\ 1000\ 0000\,$\\
    \hdashline\\
    Step 6: &amp;$WS_5          $&amp;$         1110.0001\ 0100\ 0000   $&amp;          &amp;\\
            &amp;$WC_5          $&amp;$         0011.0100\ 0000\ 0000   $&amp;          &amp;($W_{msbs}=0001\ \text{so}\ s_6=1$)\\
            &amp;$F_6=-2S_5-K_6$&amp;${\color{blue}1110.1010\ 11}00\ 0000$&amp;          &amp;$S_6={\color{blue}0000.1010\ 11}00\ 0000$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_6={\color{blue}0000.1010\ 10}00\ 0000\phantom{M}$\\
    \cline{2-3}
            &amp;$sum           $&amp;$         0011.1111\ 1000\ 0000   $&amp;$\ll1    $&amp;$K_6=0000.0000\ 0100\ 0000\ $\\
            &amp;$carry         $&amp;$         1100.0000\ 1000\ 0000   $&amp;$\ll1    $&amp;$C_6=1111.1111\ 1100\ 0000\,$\\
            &amp;                &amp;                                   &amp;          &amp;$sum+carry=0$, terminate\\
    \hdashline\\
    Terminate&amp;Square Root&amp;0.101011
\end{tabular}
\end{center}
}

{\small
\begin{center}
\begin{tabular}{cccc}
    \hdashline\\
    Step 6: &amp;$WS    $&amp;$0111.1111\ 0000\ 00$&amp;\\
            &amp;$WC    $&amp;$1000.0001\ 0000\ 00$&amp;($W_{msbs}=1111\ \text{so}\ s_6=0$)\\
            &amp;$F     $&amp;$0000.0000\ 0000\ 00$&amp;$S_6=\mathbf{1.0101\ 10}00\ 00$\\
            &amp;        &amp;                     &amp;$SM_6=\mathbf{1.0101\ 01}00\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1110\ 0000\ 00$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.0010\ 0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 7: &amp;$WS    $&amp;$1111.1100\ 0000\ 00$&amp;\\
            &amp;$WC    $&amp;$0000.0100\ 0000\ 00$&amp;($W_{msbs}=1111\ \text{so}\ s_7=0$)\\
            &amp;$F     $&amp;$0000.0000\ 0000\ 00$&amp;$S_7=\mathbf{1.0101\ 100}0\ 00$\\
            &amp;        &amp;                     &amp;$SM_7=\mathbf{1.0101\ 011}0\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1000\ 0000\ 00$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.1000\ 0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 8: &amp;$WS    $&amp;$1111.0000\ 0000\ 00$&amp;\\
            &amp;$WC    $&amp;$0001.0000\ 0000\ 00$&amp;($W_{msbs}=0000\ \text{so}\ s_8=1$)\\
            &amp;$F     $&amp;$1110.1010\ 0111\ 10$&amp;$S_8=\mathbf{1.0101\ 1001}\ 00$\\
            &amp;        &amp;                     &amp;$SM_8=\mathbf{1.0101\ 1000}\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$0000.1010\ 0111\ 10$&amp;$\ll1$\\
            &amp;$WC    $&amp;$1110.0000\ 0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 9: &amp;$WS    $&amp;$0001.0100\ 1111\ 00$&amp;\\
            &amp;$WC    $&amp;$1100.0000\ 0000\ 00$&amp;($W_{msbs}=1101\ \text{so}\ s_9=-1$)\\
            &amp;$F     $&amp;$0001.0101\ 1000\ 11$&amp;$S_9=\mathbf{1.0101\ 1000\ 1}0$\\
            &amp;        &amp;                     &amp;$SM_9=\mathbf{1.0101\ 1000\ 0}0\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1100.0001\ 0111\ 11$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0010.1001\ 0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 10:&amp;$WS    $&amp;$1000.0010\ 1111\ 10$&amp;\\
            &amp;$WC    $&amp;$0101.0010\ 0000\ 00$&amp;($W_{msbs}=1101\ \text{so}\ s_{10}=-1$)\\
            &amp;$F     $&amp;$0001.0101\ 1000\ 01$&amp;$S_{10}=\mathbf{1.0101\ 1000\ 01}$\\
            &amp;        &amp;                     &amp;$SM_{10}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1100.0001\ 0111\ 11$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0010.0101\ 0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 11:&amp;$WS    $&amp;$1000.0010\ 1111\ 10$&amp;\\
            &amp;$WC    $&amp;$0100.1010\ 0000\ 00$&amp;($W_{msbs}=1101\ \text{so}\ s_{11}=-1$)\\
            &amp;$F     $&amp;$0001.0101\ 1000\ 00$&amp;$S_{11}=\mathbf{1.0101\ 1000\ 00}$\\
            &amp;        &amp;                     &amp;$SM_{11}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1101.1101\ 0111\ 10$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.0101\ 0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 12:&amp;$WS    $&amp;$1101.1000\ 0111\ 10$&amp;\\
            &amp;$WC    $&amp;$0000.1010\ 0000\ 00$&amp;($W_{msbs}=1101\ \text{so}\ s_{12}=-1$)\\
            &amp;$F     $&amp;$0001.0101\ 1000\ 00$&amp;$S_{12}=\mathbf{1.0101\ 1000\ 00}$\\
            &amp;        &amp;                     &amp;$SM_{12}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1100.0111\ 1111\ 10$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0011.0000\ 0000\ 00$&amp;$\ll1$\\
\end{tabular}
\end{center}
}

{\small
\begin{center}
\begin{tabular}{cccc}
    Step 13:&amp;$WS    $&amp;$1000.1111\ 1111\ 00$&amp;\\
            &amp;$WC    $&amp;$0110.0000\ 0000\ 00$&amp;($W_{msbs}=1110\ \text{so}\ s_{13}=-1$)\\
            &amp;$F     $&amp;$0001.0101\ 1000\ 00$&amp;$S_{13}=\mathbf{1.0101\ 1000\ 00}$\\
            &amp;        &amp;                     &amp;$SM_{13}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1010\ 0111\ 10$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.1011\ 0000\ 00$&amp;$\ll1$\\
\end{tabular}
\end{center}
}

\vfill
\eject

{\small
\begin{center}
\begin{tabular}{ccccc}
            &amp;$X             $&amp;$         0000.1100\ 0000     $&amp;          &amp;$S_0={\color{blue}0001}.0000\ 0000\ 00$\\
            &amp;$WS=X-1        $&amp;$         1111.1100\ 0000     $&amp;          &amp;$SM_0={\color{blue}0000}.0000\ 0000\ 00\phantom{M}$\\
            &amp;$WC            $&amp;$         0000.0000\ 0000     $&amp;          &amp;$K_0=0000.0100\ 0000\ 00\ $\\
            &amp;                &amp;                               &amp;          &amp;$C_0=1111.1100\ 0000\ 00\,$\\
    \hdashline\\
    Step 1: &amp;$WS            $&amp;$         1111.1100\ 0000     $&amp;          &amp;\\
            &amp;$WC            $&amp;$         0000.0000\ 0000     $&amp;          &amp;($W_{msbs}=1111\ \text{so}\ s_1=0$)\\
            &amp;$F_1=0         $&amp;${\color{blue}0000.00}00\ 0000$&amp;          &amp;$S_1={\color{blue}0001.0}000\ 0000\ 00$\\
            &amp;                &amp;                               &amp;          &amp;$SM_1={\color{blue}0000.1}000\ 0000\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS            $&amp;$         1111.1100\ 0000     $&amp;$\ll1    $&amp;$K_1=0000.0010\ 0000\ 00\ $\\
            &amp;$WC            $&amp;$         0000.0000\ 0000     $&amp;$\ll1    $&amp;$C_1=1111.1110\ 0000\ 00\,$\\
    \hdashline\\    
    Step 2: &amp;$WS            $&amp;$         1111.1000\ 0000     $&amp;          &amp;\\
            &amp;$WC            $&amp;$         0000.0000\ 0000     $&amp;          &amp;($W_{msbs}=1111\ \text{so}\ s_2=0$)\\
            &amp;$F_2=0         $&amp;${\color{blue}0000.000}0\ 0000$&amp;          &amp;$S_2={\color{blue}0001.00}00\ 0000\ 00$\\
            &amp;                &amp;                               &amp;          &amp;$SM_2={\color{blue}0000.11}00\ 0000\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS            $&amp;$         1111.1000\ 0000     $&amp;$\ll1    $&amp;$K_2=0000.0001\ 0000\ 00\ $\\
            &amp;$WC            $&amp;$         0000.0000\ 0000     $&amp;$\ll1    $&amp;$C_2=1111.1111\ 0000\ 00\,$\\
    \hdashline\\
    Step 3: &amp;$WS            $&amp;$         1111.0000\ 0000     $&amp;          &amp;\\
            &amp;$WC            $&amp;$         0000.0000\ 0000     $&amp;          &amp;($W_{msbs}=1111\ \text{so}\ s_3=0$)\\
            &amp;$F_3=0         $&amp;${\color{blue}0000.0000}\ 0000$&amp;          &amp;$S_3={\color{blue}0001.000}0\ 0000\ 00$\\
            &amp;                &amp;                               &amp;          &amp;$SM_3={\color{blue}0000.111}0\ 0000\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS            $&amp;$1111.0000\ 0000              $&amp;$\ll1    $&amp;$K_3=0000.0000\ 1000\ 00\ $\\
            &amp;$WC            $&amp;$0000.0000\ 0000              $&amp;$\ll1    $&amp;$C_3=1111.1111\ 1000\ 00\,$\\
    \hdashline\\
    Step 4: &amp;$WS            $&amp;$1110.0000\ 0000              $&amp;          &amp;\\
            &amp;$WC            $&amp;$0000.0000\ 0000              $&amp;          &amp;($W_{msbs}=1110\ \text{so}\ s_4=-1$)\\
            &amp;$F_4=S_3-K_3   $&amp;${\color{blue}0000.1111\ 1}000$&amp;          &amp;$S_4={\color{blue}0000.1111}\ 0000\ 00$\\
            &amp;                &amp;                               &amp;          &amp;$SM_4={\color{blue}0000.1110}\ 0000\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS            $&amp;$1110.1111\ 1000              $&amp;$\ll1    $&amp;$K_4=0000.0000\ 0100\ 00\ $\\
            &amp;$WC            $&amp;$0000.0000\ 0000              $&amp;$\ll1    $&amp;$C_4=1111.1111\ 1100\ 00\,$\\
    \hdashline\\
    Step 5: &amp;$WS            $&amp;$1101.1111\ 0000              $&amp;          &amp;\\
            &amp;$WC            $&amp;$0000.0000\ 0000              $&amp;          &amp;($W_{msbs}=1101\ \text{so}\ s_5=-1$)\\
            &amp;$F_5=S_4-K_4   $&amp;${\color{blue}0000.1110\ 11}00$&amp;          &amp;$S_5={\color{blue}0000.1110\ 1}000\ 00$\\
            &amp;                &amp;                                   &amp;          &amp;$SM_5={\color{blue}0001.1110\ 0}000\ 00\phantom{M}$\\
    \cline{2-3}
            &amp;$WS            $&amp;$1101.0001\ 1100              $&amp;$\ll1    $&amp;$K_5=0000.0000\ 0010\ 00\ $\\
            &amp;$WC            $&amp;$0001.1100\ 0000              $&amp;$\ll1    $&amp;$C_5=1111.1111\ 1110\ 00\,$\\
    Terminate
\end{tabular}
\end{center}
}

\vfill
\eject

X = 0.1010101101(685/1024)

S = 0.1101000110(838/1024)

once R4 sslc gets here i can fill this in

\vfill 
\eject

X = 1.1001 (25/16)

S = 1.0100 (20/16)

{\small
\begin{center}
\begin{tabular}{cccc}
    Attempt 1:&amp; $X$ is normalized&amp; to $1/2&lt;X&lt;2$&amp;$W_{msbs}$ looks at Q4.0\\
    &amp;&amp;&amp;\\
            &amp;$X     $&amp;$0001.1001$&amp;\\
            &amp;$WS=X-1$&amp;$0000.1001$&amp; $s_0=1$\\
            &amp;$WC    $&amp;$0000.0000$&amp;$S_0=\mathbf{1}.0000,\quad SM_0=\mathbf{0}.0000$ \\
    \hdashline\\
    Step 1: &amp;$WS    $&amp;$0000.1001$&amp;\\
            &amp;$WC    $&amp;$0000.0000$&amp;($W_{msbs}=0000\ \text{so}\ s_1=1$)\\
            &amp;$F     $&amp;$1110.1100$&amp;$S_1=\mathbf{1.1}000,\quad SM_1=\mathbf{1.0}000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1110.0101$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0001.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 2: &amp;$WS    $&amp;$1100.1010$&amp;\\
            &amp;$WC    $&amp;$0010.0000$&amp;($W_{msbs}=1110\ \text{so}\ s_2=-1$)\\
            &amp;$F     $&amp;$0001.0110$&amp;$S_2=\mathbf{1.01}00,\quad SM_2=\mathbf{1.00}00$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1110$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.0010$&amp;$\ll1$\\
    \hdashline\\
    Step 3: &amp;$WS    $&amp;$1111.1100$&amp;\\
            &amp;$WC    $&amp;$0000.0100$&amp;($W_{msbs}=1111\ \text{so}\ s_3=0$)\\
            &amp;$-q_3D $&amp;$0000.0000$&amp;$S_3=\mathbf{1.010}0,\quad SM_3=\mathbf{1.001}0$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1000$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.1000$&amp;$\ll1$\\
    \hdashline\\
    Step 4: &amp;$WS    $&amp;$1111.0000$&amp;\\
            &amp;$WC    $&amp;$0001.0000$&amp;($W_{msbs}=0000\ \text{so}\ s_4=1$)\\
            &amp;$F     $&amp;$0000.0000$&amp;$S_4=\mathbf{1.0101},\quad SM_4=\mathbf{1.0100}$\\
    Terminate&amp;&amp;&amp;
\end{tabular}
\end{center}
}


{\small
\begin{center}
\begin{tabular}{cccc}
    Attempt 2:&amp; $X$ is normalized&amp; to $1/2&lt;X&lt;2$&amp;$W_{msbs}$ looks at Q3.1\\
    &amp;&amp;&amp;\\
            &amp;$X     $&amp;$001.1001$&amp;\\
            &amp;$WS=X-1$&amp;$000.1001$&amp; $s_0=1$\\
            &amp;$WC    $&amp;$000.0000$&amp;$S_0=\mathbf{1}.0000,\quad SM_0=\mathbf{0}.0000$ \\
    \hdashline\\
    Step 1: &amp;$WS    $&amp;$000.1001$&amp;\\
            &amp;$WC    $&amp;$000.0000$&amp;($W_{msbs}=000.1\ \text{so}\ s_1=1$)\\
            &amp;$F     $&amp;$110.1000$&amp;$S_1=\mathbf{1.1}000,\quad SM_1=\mathbf{1.0}000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$110.0001$&amp;$\ll1$\\
            &amp;$WC    $&amp;$001.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 2: &amp;$WS    $&amp;$100.0010$&amp;\\
            &amp;$WC    $&amp;$010.0000$&amp;($W_{msbs}=110.0\ \text{so}\ s_2=-1$)\\
            &amp;$F     $&amp;$001.0100$&amp;$S_2=\mathbf{1.01}00,\quad SM_2=\mathbf{1.00}00$\\
    \cline{2-3}
            &amp;$WS    $&amp;$111.0110$&amp;$\ll1$\\
            &amp;$WC    $&amp;$000.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 3: &amp;$WS    $&amp;$110.1100$&amp;\\
            &amp;$WC    $&amp;$000.0000$&amp;($W_{msbs}=110.1\ \text{so}\ s_3=-1$)\\
            &amp;$-q_3D $&amp;$001.0010$&amp;$S_3=\mathbf{1.001}0,\quad SM_3=\mathbf{1.000}0$\\
    \cline{2-3}
            &amp;$WS    $&amp;$111.1110$&amp;$\ll1$\\
            &amp;$WC    $&amp;$000.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 4: &amp;$WS    $&amp;$111.1110$&amp;\\
            &amp;$WC    $&amp;$000.0000$&amp;($W_{msbs}=111.1\ \text{so}\ s_4=0$)\\
            &amp;$F     $&amp;$000.0000$&amp;$S_4=\mathbf{1.0010},\quad SM_4=\mathbf{1.0001}$\\
    Terminate&amp;&amp;&amp;
\end{tabular}
\end{center}
}

{\small
\begin{center}
\begin{tabular}{cccc}
    Attempt 3:&amp; $X$ is normalized&amp; to $1&lt;X&lt;4$&amp;$W_{msbs}$ looks at Q4.0\\
    &amp;&amp;&amp;\\
            &amp;$X     $&amp;$0001.1001$&amp;\\
            &amp;$WS=X-2$&amp;$1111.1001$&amp; $s_{-1}=10$\\
            &amp;$WC    $&amp;$0000.0000$&amp;$S_{-1}=\mathbf{1}0.0000,\quad SM_{-1}=\mathbf{0}0.0000$ \\
    \hdashline\\
    Step 0: &amp;$WS    $&amp;$1111.1001$&amp;\\
            &amp;$WC    $&amp;$0000.0000$&amp;($W_{msbs}=1111\ \text{so}\ s_0=0$)\\
            &amp;$F     $&amp;$0000.0000$&amp;$S_0=\mathbf{10}.0000,\quad SM_0=\mathbf{01}.0000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1001$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 1: &amp;$WS    $&amp;$1111.0010$&amp;\\
            &amp;$WC    $&amp;$0000.0000$&amp;($W_{msbs}=1111\ \text{so}\ s_1=0$)\\
            &amp;$F     $&amp;$0000.0000$&amp;$S_1=\mathbf{10.0}000,\quad SM_1=\mathbf{01.1}000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.0010$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 2: &amp;$WS    $&amp;$1110.0100$&amp;\\
            &amp;$WC    $&amp;$0000.0000$&amp;($W_{msbs}=1110\ \text{so}\ s_2=-1$)\\
            &amp;$-q_3D $&amp;$0001.1100$&amp;$S_2=\mathbf{01.01}00,\quad SM_2=\mathbf{01.00}00$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1000$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.1000$&amp;$\ll1$\\
    Terminate&amp;&amp;&amp;
\end{tabular}
\end{center}
}

\vfill
\eject

X = 0.011001 (25/64)

S = 0.101000 (40/64)

{\small
\begin{center}
\begin{tabular}{cccc}
    Attempt 4:&amp; $X$ is normalized&amp; to $1/4&lt;X&lt;1$&amp;$W_{msbs}$ looks at Q3.1\\
    &amp;&amp;&amp;\\
            &amp;$X     $&amp;$000.0110\ 01$&amp;\\
            &amp;$WS=X-1$&amp;$111.0110\ 01$&amp; $s_0=1$\\
            &amp;$WC    $&amp;$000.0000\ 00$&amp;$S_0=\mathbf{1}.000000,\quad SM_0=\mathbf{0}.000000$ \\
    \hdashline\\
    Step 1: &amp;$WS    $&amp;$111.0110\ 01$&amp;\\
            &amp;$WC    $&amp;$000.0000\ 00$&amp;($W_{msbs}=111.0\ \text{so}\ s_1=-1$)\\
            &amp;$F     $&amp;$000.1000\ 00$&amp;$S_1=\mathbf{0.1}00000,\quad SM_1=\mathbf{0.0}00000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$111.1110\ 01$&amp;$\ll1$\\
            &amp;$WC    $&amp;$000.0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 2: &amp;$WS    $&amp;$111.1100\ 10$&amp;\\
            &amp;$WC    $&amp;$000.0000\ 00$&amp;($W_{msbs}=111.1\ \text{so}\ s_2=0$)\\
            &amp;$F     $&amp;$000.0000\ 00$&amp;$S_2=\mathbf{0.10}0000,\quad SM_2=\mathbf{0.01}0000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$111.1100\ 10$&amp;$\ll1$\\
            &amp;$WC    $&amp;$000.0000\ 00$&amp;$\ll1$\\
    \hdashline\\
    Step 3: &amp;$WS    $&amp;$111.1001\ 00$&amp;\\
            &amp;$WC    $&amp;$000.0000\ 00$&amp;($W_{msbs}=010.0\ \text{so}\ s_3=1$)\\
            &amp;$-q_3D $&amp;$111.0010\ 00$&amp;$S_3=\mathbf{0.111}000,\quad SM_3=\mathbf{0.110}000$\\
    \cline{2-3}
            &amp;$WS    $&amp;$1111.1110$&amp;$\ll1$\\
            &amp;$WC    $&amp;$0000.0000$&amp;$\ll1$\\
    \hdashline\\
    Step 4: &amp;$WS    $&amp;$1111.1110$&amp;\\
            &amp;$WC    $&amp;$0000.0000$&amp;($W_{msbs}=111.1\ \text{so}\ s_4=0$)\\
            &amp;$F     $&amp;$0000.0000$&amp;$S_4=\mathbf{1.0010}00,\quad SM_4=\mathbf{1.0001}00$\\
    Terminate&amp;&amp;&amp;
\end{tabular}
\end{center}
}


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