\documentclass[12pt]{article} \usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox} \usepackage{arydshln} \parskip = .2in \parindent = 0in \pagestyle{empty} %========== %========== \begin{document} X = 1.0000\ 1101 (269/256) D = 1.0011\ 0110 (310/256) Q = 0.1101\ 1110 (222/256) D[1.3] = 1.001, so we use the ``1.001" column of chart 13.X. This means we select a quotient bit of 2 if the partial remainder is greater than or equal to 3.5, a quotient bit of 1 if the partial is greater or equal to than 1.0, a zero if the partial is greater than or equal to -1.5, -1 if the partial is greater than or equal to -3.75, and a -2 otherwise. {\small \begin{center} \begin{tabular}{cccc} Initialization&$D$&$0001.0011\ 0110\ 00$&\\ &$2D$&$0010.0110\ 1100\ 00$&\\ &$-D=\overline{D}+1$&$1110.1100\ 1001\ 11$&(+ 1 ulp)\\ &$-2D=\overline{2D}+1$&$1101.1001\ 0011\ 11$&(+ 1 ulp)\\ &&&\\ &$WS_{-1}=X$&$0001.0000\ 1101\ 00$&\\ &$WC_{-1}$&$0000.0000\ 0000\ 00$&\\ \hdashline\\ Step 0: &$WS_{-1} $&$0001.0000\ 1101\ 00$&\\ &$WC_{-1} $&$0000.0000\ 0000\ 0\mathbf{1}$&($W_{msbs}=0001.000\ \text{so}\ q_0=1$)\\ &$-q_0D $&$1110.1100\ 1001\ 11$&\\ \cline{2-3} &$sum $&$1111.1100\ 0100\ 10$&$\ll2$\\ &$carry $&$0000.0001\ 0010\ 10$&$\ll2$\\ \hdashline\\ Step 1: &$WS_0 $&$1111.0001\ 0010\ 00$&\\ &$WC_0 $&$0000.0100\ 1010\ 0\mathbf{0}$&($W_{msbs}=1111.010\ \text{so}\ q_1=-1$)\\ &$-q_1D $&$0001.0011\ 0110\ 00$&\\ \cline{2-3} &$sum $&$1110.0110\ 1110\ 00$&$\ll2$\\ &$carry $&$0010.0010\ 0100\ 00$&$\ll2$\\ \hdashline\\ Step 2: &$WS_1 $&$1001.1011\ 1000\ 00$&\\ &$WC_1 $&$1000.1001\ 0000\ 0\mathbf{1}$&($W_{msbs}=0010.010\ \text{so}\ q_2=2$)\\ &$-q_2D $&$1101.1001\ 0011\ 11$\\ \cline{2-3} &$sum $&$1100.1011\ 1011\ 10$&$\ll2$\\ &$carry $&$0011.0010\ 0000\ 10$&$\ll2$\\ \hdashline\\ Step 3: &$WS_2 $&$0010.1110\ 1110\ 00$&\\ &$WC_2 $&$1100.1000\ 0010\ 0\mathbf{0}$&($W_{msbs}=1111.011\ \text{so}\ q_3=-1$)\\ &$-q_3D $&$0001.0011\ 0110\ 00$\\ \cline{2-3} &$sum $&$1111.0101\ 1010\ 00$&$\ll2$\\ &$carry $&$0001.0100\ 0100\ 00$&$\ll2$\\ \hdashline\\ Step 4: &$WS_3 $&$1101.0110\ 1000\ 00$&\\ &$WC_3 $&$0101.0001\ 0000\ 0\mathbf{1}$&($W_{msbs}=0010.011\ \text{so}\ q_4=2$)\\ &$-q_4D $&$1101.1001\ 0011\ 11$\\ \cline{2-3} &$sum $&$0101.1110\ 1011\ 10$&$\ll2$\\ &$carry $&$1010.0010\ 0000\ 10$&$\ll2$\\ \hdashline\\ Step 5: &$WS_4 $&$0111.1010\ 1110\ 00$&\\ &$WC_4 $&$1000.1000\ 0010\ 0\mathbf{0}$&($W_{msbs}=0000.001\ \text{so}\ q_5=0$)\\ &$-q_5D $&$0000.0000\ 0000\ 00$\\ \cline{2-3} &$sum $&$1111.0010\ 1100\ 00$&$\ll2$\\ &$carry $&$0001.0000\ 0100\ 00$&$\ll2$\\ \hdashline\\ Terminate&Quotient&$00.11\ 01\ 11\ 10\ (00\ 1)$ \end{tabular} \end{center} } \end{document}