mirror of
https://github.com/openhwgroup/cvw
synced 2025-02-11 06:05:49 +00:00
85 lines
3.1 KiB
TeX
85 lines
3.1 KiB
TeX
\documentclass[12pt]{article}
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\usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox}
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\usepackage{arydshln}
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\parskip = .2in
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\parindent = 0in
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\pagestyle{empty}
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%==========
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%==========
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\begin{document}
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X = 1.0000\ 1101 (269/256)
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D = 1.0011\ 0110 (310/256)
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Q = 0.1101\ 1110 (222/256)
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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.
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{\small
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\begin{center}
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\begin{tabular}{cccc}
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Initialization&$D$&$0001.0011\ 0110\ 00$&\\
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&$2D$&$0010.0110\ 1100\ 00$&\\
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&$-D=\overline{D}+1$&$1110.1100\ 1001\ 11$&(+ 1 ulp)\\
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&$-2D=\overline{2D}+1$&$1101.1001\ 0011\ 11$&(+ 1 ulp)\\
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&&&\\
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&$WS_{-1}=X$&$0001.0000\ 1101\ 00$&\\
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&$WC_{-1}$&$0000.0000\ 0000\ 00$&\\
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\hdashline\\
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Step 0: &$WS_{-1} $&$0001.0000\ 1101\ 00$&\\
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&$WC_{-1} $&$0000.0000\ 0000\ 0\mathbf{1}$&($W_{msbs}=0001.000\ \text{so}\ q_0=1$)\\
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&$-q_0D $&$1110.1100\ 1001\ 11$&\\
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\cline{2-3}
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&$sum $&$1111.1100\ 0100\ 10$&$\ll2$\\
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&$carry $&$0000.0001\ 0010\ 10$&$\ll2$\\
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\hdashline\\
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Step 1: &$WS_0 $&$1111.0001\ 0010\ 00$&\\
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&$WC_0 $&$0000.0100\ 1010\ 0\mathbf{0}$&($W_{msbs}=1111.010\ \text{so}\ q_1=-1$)\\
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&$-q_1D $&$0001.0011\ 0110\ 00$&\\
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\cline{2-3}
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&$sum $&$1110.0110\ 1110\ 00$&$\ll2$\\
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&$carry $&$0010.0010\ 0100\ 00$&$\ll2$\\
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\hdashline\\
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Step 2: &$WS_1 $&$1001.1011\ 1000\ 00$&\\
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&$WC_1 $&$1000.1001\ 0000\ 0\mathbf{1}$&($W_{msbs}=0010.010\ \text{so}\ q_2=2$)\\
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&$-q_2D $&$1101.1001\ 0011\ 11$\\
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\cline{2-3}
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&$sum $&$1100.1011\ 1011\ 10$&$\ll2$\\
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&$carry $&$0011.0010\ 0000\ 10$&$\ll2$\\
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\hdashline\\
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Step 3: &$WS_2 $&$0010.1110\ 1110\ 00$&\\
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&$WC_2 $&$1100.1000\ 0010\ 0\mathbf{0}$&($W_{msbs}=1111.011\ \text{so}\ q_3=-1$)\\
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&$-q_3D $&$0001.0011\ 0110\ 00$\\
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\cline{2-3}
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&$sum $&$1111.0101\ 1010\ 00$&$\ll2$\\
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&$carry $&$0001.0100\ 0100\ 00$&$\ll2$\\
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\hdashline\\
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Step 4: &$WS_3 $&$1101.0110\ 1000\ 00$&\\
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&$WC_3 $&$0101.0001\ 0000\ 0\mathbf{1}$&($W_{msbs}=0010.011\ \text{so}\ q_4=2$)\\
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&$-q_4D $&$1101.1001\ 0011\ 11$\\
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\cline{2-3}
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&$sum $&$0101.1110\ 1011\ 10$&$\ll2$\\
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&$carry $&$1010.0010\ 0000\ 10$&$\ll2$\\
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\hdashline\\
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Step 5: &$WS_4 $&$0111.1010\ 1110\ 00$&\\
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&$WC_4 $&$1000.1000\ 0010\ 0\mathbf{0}$&($W_{msbs}=0000.001\ \text{so}\ q_5=0$)\\
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&$-q_5D $&$0000.0000\ 0000\ 00$\\
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\cline{2-3}
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&$sum $&$1111.0010\ 1100\ 00$&$\ll2$\\
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&$carry $&$0001.0000\ 0100\ 00$&$\ll2$\\
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\hdashline\\
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Terminate&Quotient&$00.11\ 01\ 11\ 10\ (00\ 1)$
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\end{tabular}
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\end{center}
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}
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\end{document}
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