need to re-read and spellcheck

7 files changed, 702 insertions, 635 deletions

diff --git a/report/debug_table.tex b/report/debug_table.tex
new file mode 100644
index 0000000..0f30877
--- /dev/null
+++ b/report/debug_table.tex
@@ -0,0 +1,24 @@
+\begin{longtable}{llrrlrll}
+\hline
+ multiplicand bin   & multiplier bin   &   multiplicand dec &   multiplier dec & expected bin               &   expected dec & booth   & mod booth   \\
+\hline
+\endhead
+ 0b1110             & 0b1111           &                 -2 &               -1 & 0b10                       &              2 & PASS    & PASS        \\
+ 0b101              & 0b0              &                  5 &                0 & 0b0                        &              0 & PASS    & PASS        \\
+ 0b111111           & 0b111111         &                 -1 &               -1 & 0b1                        &              1 & PASS    & PASS        \\
+ 0b101110           & 0b110111         &                -18 &               -9 & 0b10100010                 &            162 & PASS    & PASS        \\
+ 0b111011           & 0b100011         &                 -5 &              -29 & 0b10010001                 &            145 & PASS    & PASS        \\
+ 0b11111            & 0b1010101        &                 31 &               85 & 0b101001001011             &           2635 & PASS    & PASS        \\
+ 0b11010111         & 0b1010101        &                -41 &               85 & 0b1111001001100011         &          -3485 & PASS    & PASS        \\
+ 0b1010101          & 0b11010111       &                 85 &              -41 & 0b1111001001100011         &          -3485 & PASS    & PASS        \\
+ 0b1110111          & 0b110011         &                119 &               51 & 0b1011110110101            &           6069 & PASS    & PASS        \\
+ 0b0                & 0b1110111        &                  0 &              119 & 0b0                        &              0 & PASS    & PASS        \\
+ 0b101010101        & 0b101010101      &                341 &              341 & 0b11100011000111001        &         116281 & PASS    & PASS        \\
+ 0b1100111011       & 0b1001110000     &               -197 &             -400 & 0b10011001111010000        &          78800 & PASS    & PASS        \\
+ 0b1001101110       & 0b101111010      &               -402 &              378 & 0b11011010111001101100     &        -151956 & PASS    & PASS        \\
+ 0b10101010101      & 0b10101010101    &               1365 &             1365 & 0b111000110111000111001    &        1863225 & PASS    & PASS        \\
+ 0b1111100111       & 0b0              &                999 &                0 & 0b0                        &              0 & PASS    & PASS        \\
+ 0b101010101010     & 0b101010101010   &              -1366 &            -1366 & 0b111000111100011100100    &        1865956 & PASS    & PASS        \\
+ 0b111001110000     & 0b11111111       &               -400 &              255 & 0b111111100111000110010000 &        -102000 & PASS    & PASS        \\
+\hline
+\end{longtable}
\ No newline at end of file
diff --git a/report/iterations.pgf b/report/iterations.pgf
index 2084aa3..52d794f 100644
--- a/report/iterations.pgf
+++ b/report/iterations.pgf
@@ -27,7 +27,7 @@
 \begingroup%
 \makeatletter%
 \begin{pgfpicture}%
-\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.500000in}{3.500000in}}%
 \pgfusepath{use as bounding box, clip}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -39,9 +39,9 @@
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}%
+\pgfpathlineto{\pgfqpoint{4.500000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.500000in}{3.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{3.500000in}}%
 \pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
 \pgfpathclose%
 \pgfusepath{fill}%
@@ -56,11 +56,11 @@
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
-\pgfpathlineto{\pgfqpoint{0.800000in}{4.224000in}}%
-\pgfpathlineto{\pgfqpoint{0.800000in}{0.528000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
+\pgfpathlineto{\pgfqpoint{0.562500in}{3.080000in}}%
+\pgfpathlineto{\pgfqpoint{0.562500in}{0.385000in}}%
 \pgfpathclose%
 \pgfusepath{fill}%
 \end{pgfscope}%
@@ -79,7 +79,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.528000in}%
+\pgfsys@transformshift{0.721023in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -87,7 +87,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.025455in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
+\pgftext[x=0.721023in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -104,7 +104,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.589091in}{0.528000in}%
+\pgfsys@transformshift{1.513636in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -112,7 +112,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.589091in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{5}$}}%
+\pgftext[x=1.513636in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -129,7 +129,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{0.528000in}%
+\pgfsys@transformshift{2.306250in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -137,7 +137,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=2.152727in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
+\pgftext[x=2.306250in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -154,7 +154,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.716364in}{0.528000in}%
+\pgfsys@transformshift{3.098864in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -162,7 +162,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=2.716364in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{7}$}}%
+\pgftext[x=3.098864in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -179,7 +179,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{0.528000in}%
+\pgfsys@transformshift{3.891477in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -187,113 +187,13 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=3.280000in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{3.843636in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=3.843636in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{9}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=4.407273in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{4.970909in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=4.970909in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{11}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=5.534545in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
+\pgftext[x=3.891477in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=3.280000in,y=0.251766in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Operand Length}}%
+\pgftext[x=2.306250in,y=0.108766in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Operand Length}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -310,7 +210,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{0.696000in}%
+\pgfsys@transformshift{0.562500in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -318,7 +218,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=0.647775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
+\pgftext[x=0.395833in, y=0.459275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -335,7 +235,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{1.368000in}%
+\pgfsys@transformshift{0.562500in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -343,7 +243,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=1.319775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
+\pgftext[x=0.395833in, y=0.949275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -360,7 +260,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{2.040000in}%
+\pgfsys@transformshift{0.562500in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -368,7 +268,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=1.991775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
+\pgftext[x=0.395833in, y=1.439275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -385,7 +285,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{2.712000in}%
+\pgfsys@transformshift{0.562500in}{1.977500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -393,7 +293,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=2.663775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
+\pgftext[x=0.395833in, y=1.929275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -410,7 +310,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{3.384000in}%
+\pgfsys@transformshift{0.562500in}{2.467500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -418,7 +318,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.563888in, y=3.335775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
+\pgftext[x=0.326388in, y=2.419275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -435,7 +335,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{4.056000in}%
+\pgfsys@transformshift{0.562500in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -443,16 +343,16 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.563888in, y=4.007775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
+\pgftext[x=0.326388in, y=2.909275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.508333in,y=2.376000in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of iterations}}%
+\pgftext[x=0.270833in,y=1.732500in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of iterations}}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetroundjoin%
@@ -460,27 +360,27 @@
 \definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{1.025455in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{1.025455in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{2.040000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{2.040000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{2.040000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{3.384000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{3.384000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{3.384000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
+\pgfpathmoveto{\pgfqpoint{0.721023in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{0.721023in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.487500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.487500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.487500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{2.467500in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{2.467500in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{2.467500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetmiterjoin%
@@ -499,76 +399,76 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{1.368000in}%
+\pgfsys@transformshift{0.721023in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{1.368000in}%
+\pgfsys@transformshift{0.721023in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{2.040000in}%
+\pgfsys@transformshift{1.513636in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{2.040000in}%
+\pgfsys@transformshift{1.513636in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{2.040000in}%
+\pgfsys@transformshift{1.513636in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.712000in}%
+\pgfsys@transformshift{2.306250in}{1.977500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.712000in}%
+\pgfsys@transformshift{2.306250in}{1.977500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.712000in}%
+\pgfsys@transformshift{2.306250in}{1.977500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.712000in}%
+\pgfsys@transformshift{2.306250in}{1.977500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.712000in}%
+\pgfsys@transformshift{2.306250in}{1.977500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{3.384000in}%
+\pgfsys@transformshift{3.098864in}{2.467500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{3.384000in}%
+\pgfsys@transformshift{3.098864in}{2.467500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{3.384000in}%
+\pgfsys@transformshift{3.098864in}{2.467500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{4.056000in}%
+\pgfsys@transformshift{3.891477in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{4.056000in}%
+\pgfsys@transformshift{3.891477in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{4.056000in}%
+\pgfsys@transformshift{3.891477in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{4.056000in}%
+\pgfsys@transformshift{3.891477in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetroundjoin%
@@ -576,27 +476,27 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{1.025455in}{0.696000in}}%
-\pgfpathlineto{\pgfqpoint{1.025455in}{0.696000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.032000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.032000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.032000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{1.704000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{1.704000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{1.704000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
+\pgfpathmoveto{\pgfqpoint{0.721023in}{0.507500in}}%
+\pgfpathlineto{\pgfqpoint{0.721023in}{0.507500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{0.752500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{0.752500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{0.752500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.242500in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.242500in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.242500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetmiterjoin%
@@ -615,71 +515,71 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.696000in}%
+\pgfsys@transformshift{0.721023in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.696000in}%
+\pgfsys@transformshift{0.721023in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.032000in}%
+\pgfsys@transformshift{1.513636in}{0.752500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.032000in}%
+\pgfsys@transformshift{1.513636in}{0.752500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.032000in}%
+\pgfsys@transformshift{1.513636in}{0.752500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.368000in}%
+\pgfsys@transformshift{2.306250in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.368000in}%
+\pgfsys@transformshift{2.306250in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.368000in}%
+\pgfsys@transformshift{2.306250in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.368000in}%
+\pgfsys@transformshift{2.306250in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.368000in}%
+\pgfsys@transformshift{2.306250in}{0.997500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{1.704000in}%
+\pgfsys@transformshift{3.098864in}{1.242500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{1.704000in}%
+\pgfsys@transformshift{3.098864in}{1.242500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{1.704000in}%
+\pgfsys@transformshift{3.098864in}{1.242500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{2.040000in}%
+\pgfsys@transformshift{3.891477in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{2.040000in}%
+\pgfsys@transformshift{3.891477in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{2.040000in}%
+\pgfsys@transformshift{3.891477in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{2.040000in}%
+\pgfsys@transformshift{3.891477in}{1.487500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -690,8 +590,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{0.800000in}{4.224000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{0.562500in}{3.080000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -701,8 +601,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{5.760000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
+\pgfpathmoveto{\pgfqpoint{4.050000in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -712,8 +612,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{0.528000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{0.385000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -723,8 +623,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{4.224000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{3.080000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -738,16 +638,16 @@
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetstrokeopacity{0.800000}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.897222in}{3.725543in}}%
-\pgfpathlineto{\pgfqpoint{2.990205in}{3.725543in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{3.017983in}{3.725543in}}{\pgfqpoint{3.017983in}{3.753321in}}%
-\pgfpathlineto{\pgfqpoint{3.017983in}{4.126778in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{3.017983in}{4.154556in}}{\pgfqpoint{2.990205in}{4.154556in}}%
-\pgfpathlineto{\pgfqpoint{0.897222in}{4.154556in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{0.869444in}{4.154556in}}{\pgfqpoint{0.869444in}{4.126778in}}%
-\pgfpathlineto{\pgfqpoint{0.869444in}{3.753321in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{0.869444in}{3.725543in}}{\pgfqpoint{0.897222in}{3.725543in}}%
-\pgfpathlineto{\pgfqpoint{0.897222in}{3.725543in}}%
+\pgfpathmoveto{\pgfqpoint{0.659722in}{2.581543in}}%
+\pgfpathlineto{\pgfqpoint{2.752705in}{2.581543in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.780483in}{2.581543in}}{\pgfqpoint{2.780483in}{2.609321in}}%
+\pgfpathlineto{\pgfqpoint{2.780483in}{2.982778in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.780483in}{3.010556in}}{\pgfqpoint{2.752705in}{3.010556in}}%
+\pgfpathlineto{\pgfqpoint{0.659722in}{3.010556in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.631944in}{3.010556in}}{\pgfqpoint{0.631944in}{2.982778in}}%
+\pgfpathlineto{\pgfqpoint{0.631944in}{2.609321in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.631944in}{2.581543in}}{\pgfqpoint{0.659722in}{2.581543in}}%
+\pgfpathlineto{\pgfqpoint{0.659722in}{2.581543in}}%
 \pgfpathclose%
 \pgfusepath{stroke,fill}%
 \end{pgfscope}%
@@ -758,9 +658,9 @@
 \definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{0.925000in}{4.050389in}}%
-\pgfpathlineto{\pgfqpoint{1.063889in}{4.050389in}}%
-\pgfpathlineto{\pgfqpoint{1.202778in}{4.050389in}}%
+\pgfpathmoveto{\pgfqpoint{0.687500in}{2.906389in}}%
+\pgfpathlineto{\pgfqpoint{0.826389in}{2.906389in}}%
+\pgfpathlineto{\pgfqpoint{0.965278in}{2.906389in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -781,7 +681,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.063889in}{4.050389in}%
+\pgfsys@transformshift{0.826389in}{2.906389in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -789,7 +689,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.313889in,y=4.001778in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}booths algorithim}}%
+\pgftext[x=1.076389in,y=2.857778in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}booths algorithim}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -798,9 +698,9 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{0.925000in}{3.856716in}}%
-\pgfpathlineto{\pgfqpoint{1.063889in}{3.856716in}}%
-\pgfpathlineto{\pgfqpoint{1.202778in}{3.856716in}}%
+\pgfpathmoveto{\pgfqpoint{0.687500in}{2.712716in}}%
+\pgfpathlineto{\pgfqpoint{0.826389in}{2.712716in}}%
+\pgfpathlineto{\pgfqpoint{0.965278in}{2.712716in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -821,7 +721,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.063889in}{3.856716in}%
+\pgfsys@transformshift{0.826389in}{2.712716in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -829,7 +729,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.313889in,y=3.808105in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}modified booths algorithim}}%
+\pgftext[x=1.076389in,y=2.664105in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}modified booths algorithim}}%
 \end{pgfscope}%
 \end{pgfpicture}%
 \makeatother%
diff --git a/report/performance.pgf b/report/performance.pgf
index 0d2aaab..8d386e9 100644
--- a/report/performance.pgf
+++ b/report/performance.pgf
@@ -27,7 +27,7 @@
 \begingroup%
 \makeatletter%
 \begin{pgfpicture}%
-\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.500000in}{3.500000in}}%
 \pgfusepath{use as bounding box, clip}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -39,9 +39,9 @@
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}%
+\pgfpathlineto{\pgfqpoint{4.500000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.500000in}{3.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{3.500000in}}%
 \pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
 \pgfpathclose%
 \pgfusepath{fill}%
@@ -56,11 +56,11 @@
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
-\pgfpathlineto{\pgfqpoint{0.800000in}{4.224000in}}%
-\pgfpathlineto{\pgfqpoint{0.800000in}{0.528000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
+\pgfpathlineto{\pgfqpoint{0.562500in}{3.080000in}}%
+\pgfpathlineto{\pgfqpoint{0.562500in}{0.385000in}}%
 \pgfpathclose%
 \pgfusepath{fill}%
 \end{pgfscope}%
@@ -79,7 +79,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.528000in}%
+\pgfsys@transformshift{0.721023in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -87,7 +87,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.025455in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
+\pgftext[x=0.721023in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -104,7 +104,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.589091in}{0.528000in}%
+\pgfsys@transformshift{1.513636in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -112,7 +112,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.589091in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{5}$}}%
+\pgftext[x=1.513636in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -129,7 +129,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{0.528000in}%
+\pgfsys@transformshift{2.306250in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -137,7 +137,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=2.152727in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
+\pgftext[x=2.306250in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -154,7 +154,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.716364in}{0.528000in}%
+\pgfsys@transformshift{3.098864in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -162,7 +162,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=2.716364in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{7}$}}%
+\pgftext[x=3.098864in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -179,7 +179,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{0.528000in}%
+\pgfsys@transformshift{3.891477in}{0.385000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -187,113 +187,13 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=3.280000in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{3.843636in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
+\pgftext[x=3.891477in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=3.843636in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{9}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=4.407273in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{4.970909in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=4.970909in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{11}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\pgfsetbuttcap%
-\pgfsetroundjoin%
-\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetfillcolor{currentfill}%
-\pgfsetlinewidth{0.803000pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{currentstroke}%
-\pgfsetdash{}{0pt}%
-\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
-\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
-\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
-\pgfusepath{stroke,fill}%
-}%
-\begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{0.528000in}%
-\pgfsys@useobject{currentmarker}{}%
-\end{pgfscope}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=5.534545in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
-\end{pgfscope}%
-\begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=3.280000in,y=0.251766in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Length of Operands}}%
+\pgftext[x=2.306250in,y=0.108766in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Length of Operands}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -310,7 +210,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{0.696000in}%
+\pgfsys@transformshift{0.562500in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -318,7 +218,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=0.647775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{0}$}}%
+\pgftext[x=0.395833in, y=0.459275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{0}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -335,7 +235,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{1.256000in}%
+\pgfsys@transformshift{0.562500in}{0.915833in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -343,7 +243,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=1.207775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
+\pgftext[x=0.395833in, y=0.867608in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -360,7 +260,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{1.816000in}%
+\pgfsys@transformshift{0.562500in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -368,7 +268,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=1.767775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
+\pgftext[x=0.395833in, y=1.275941in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -385,7 +285,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{2.376000in}%
+\pgfsys@transformshift{0.562500in}{1.732500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -393,7 +293,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=2.327775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
+\pgftext[x=0.395833in, y=1.684275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -410,7 +310,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{2.936000in}%
+\pgfsys@transformshift{0.562500in}{2.140833in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -418,7 +318,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.633333in, y=2.887775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
+\pgftext[x=0.395833in, y=2.092608in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -435,7 +335,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{3.496000in}%
+\pgfsys@transformshift{0.562500in}{2.549167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -443,7 +343,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.563888in, y=3.447775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
+\pgftext[x=0.326388in, y=2.500941in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -460,7 +360,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{0.800000in}{4.056000in}%
+\pgfsys@transformshift{0.562500in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -468,16 +368,16 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.563888in, y=4.007775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
+\pgftext[x=0.326388in, y=2.909275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=0.508333in,y=2.376000in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of Additions and Subtractions}}%
+\pgftext[x=0.270833in,y=1.732500in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of Additions and Subtractions}}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetroundjoin%
@@ -485,27 +385,27 @@
 \definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{1.025455in}{0.976000in}}%
-\pgfpathlineto{\pgfqpoint{1.025455in}{0.696000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{0.976000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.536000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.536000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.936000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.936000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{2.096000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{3.496000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{1.536000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{2.376000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{0.696000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{3.776000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{1.256000in}}%
+\pgfpathmoveto{\pgfqpoint{0.721023in}{0.711667in}}%
+\pgfpathlineto{\pgfqpoint{0.721023in}{0.507500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{0.711667in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.120000in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.120000in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{2.140833in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{2.140833in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.528333in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{2.549167in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.120000in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.732500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{0.507500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{2.753333in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{0.915833in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetmiterjoin%
@@ -524,76 +424,76 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.976000in}%
+\pgfsys@transformshift{0.721023in}{0.711667in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.696000in}%
+\pgfsys@transformshift{0.721023in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{0.976000in}%
+\pgfsys@transformshift{1.513636in}{0.711667in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.536000in}%
+\pgfsys@transformshift{1.513636in}{1.120000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.536000in}%
+\pgfsys@transformshift{1.513636in}{1.120000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.936000in}%
+\pgfsys@transformshift{2.306250in}{2.140833in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.936000in}%
+\pgfsys@transformshift{2.306250in}{2.140833in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{2.096000in}%
+\pgfsys@transformshift{2.306250in}{1.528333in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{3.496000in}%
+\pgfsys@transformshift{3.098864in}{2.549167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{1.536000in}%
+\pgfsys@transformshift{3.098864in}{1.120000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{2.376000in}%
+\pgfsys@transformshift{3.098864in}{1.732500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{4.056000in}%
+\pgfsys@transformshift{3.891477in}{2.957500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{0.696000in}%
+\pgfsys@transformshift{3.891477in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{3.776000in}%
+\pgfsys@transformshift{3.891477in}{2.753333in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{1.256000in}%
+\pgfsys@transformshift{3.891477in}{0.915833in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetroundjoin%
@@ -601,27 +501,27 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{1.025455in}{0.976000in}}%
-\pgfpathlineto{\pgfqpoint{1.025455in}{0.696000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{0.976000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.536000in}}%
-\pgfpathlineto{\pgfqpoint{2.152727in}{1.536000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{3.280000in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{2.096000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{1.536000in}}%
-\pgfpathlineto{\pgfqpoint{4.407273in}{1.816000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{2.376000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{0.696000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{2.376000in}}%
-\pgfpathlineto{\pgfqpoint{5.534545in}{1.256000in}}%
+\pgfpathmoveto{\pgfqpoint{0.721023in}{0.711667in}}%
+\pgfpathlineto{\pgfqpoint{0.721023in}{0.507500in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{0.711667in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.120000in}}%
+\pgfpathlineto{\pgfqpoint{1.513636in}{1.120000in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{2.306250in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.528333in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.120000in}}%
+\pgfpathlineto{\pgfqpoint{3.098864in}{1.324167in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{1.732500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{0.507500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{1.732500in}}%
+\pgfpathlineto{\pgfqpoint{3.891477in}{0.915833in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
+\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
 \pgfusepath{clip}%
 \pgfsetbuttcap%
 \pgfsetmiterjoin%
@@ -640,71 +540,71 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.976000in}%
+\pgfsys@transformshift{0.721023in}{0.711667in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.025455in}{0.696000in}%
+\pgfsys@transformshift{0.721023in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{0.976000in}%
+\pgfsys@transformshift{1.513636in}{0.711667in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.536000in}%
+\pgfsys@transformshift{1.513636in}{1.120000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.152727in}{1.536000in}%
+\pgfsys@transformshift{1.513636in}{1.120000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.280000in}{1.816000in}%
+\pgfsys@transformshift{2.306250in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{2.096000in}%
+\pgfsys@transformshift{3.098864in}{1.528333in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{1.536000in}%
+\pgfsys@transformshift{3.098864in}{1.120000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{4.407273in}{1.816000in}%
+\pgfsys@transformshift{3.098864in}{1.324167in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{2.376000in}%
+\pgfsys@transformshift{3.891477in}{1.732500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{0.696000in}%
+\pgfsys@transformshift{3.891477in}{0.507500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{2.376000in}%
+\pgfsys@transformshift{3.891477in}{1.732500in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{5.534545in}{1.256000in}%
+\pgfsys@transformshift{3.891477in}{0.915833in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -715,8 +615,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{0.800000in}{4.224000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{0.562500in}{3.080000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -726,8 +626,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{5.760000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
+\pgfpathmoveto{\pgfqpoint{4.050000in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -737,8 +637,8 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{0.528000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{0.385000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -748,17 +648,11 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.800000in}{4.224000in}}%
-\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
+\pgfpathmoveto{\pgfqpoint{0.562500in}{3.080000in}}%
+\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
-\pgfsetstrokecolor{textcolor}%
-\pgfsetfillcolor{textcolor}%
-\pgftext[x=3.280000in,y=4.307333in,,base]{\color{textcolor}{\rmfamily\fontsize{12.000000}{14.400000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Operations vs Operand Length}}%
-\end{pgfscope}%
-\begin{pgfscope}%
 \pgfsetbuttcap%
 \pgfsetmiterjoin%
 \definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
@@ -769,16 +663,16 @@
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetstrokeopacity{0.800000}%
 \pgfsetdash{}{0pt}%
-\pgfpathmoveto{\pgfqpoint{0.897222in}{3.725543in}}%
-\pgfpathlineto{\pgfqpoint{2.990205in}{3.725543in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{3.017983in}{3.725543in}}{\pgfqpoint{3.017983in}{3.753321in}}%
-\pgfpathlineto{\pgfqpoint{3.017983in}{4.126778in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{3.017983in}{4.154556in}}{\pgfqpoint{2.990205in}{4.154556in}}%
-\pgfpathlineto{\pgfqpoint{0.897222in}{4.154556in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{0.869444in}{4.154556in}}{\pgfqpoint{0.869444in}{4.126778in}}%
-\pgfpathlineto{\pgfqpoint{0.869444in}{3.753321in}}%
-\pgfpathquadraticcurveto{\pgfqpoint{0.869444in}{3.725543in}}{\pgfqpoint{0.897222in}{3.725543in}}%
-\pgfpathlineto{\pgfqpoint{0.897222in}{3.725543in}}%
+\pgfpathmoveto{\pgfqpoint{0.659722in}{2.581543in}}%
+\pgfpathlineto{\pgfqpoint{2.752705in}{2.581543in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.780483in}{2.581543in}}{\pgfqpoint{2.780483in}{2.609321in}}%
+\pgfpathlineto{\pgfqpoint{2.780483in}{2.982778in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.780483in}{3.010556in}}{\pgfqpoint{2.752705in}{3.010556in}}%
+\pgfpathlineto{\pgfqpoint{0.659722in}{3.010556in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.631944in}{3.010556in}}{\pgfqpoint{0.631944in}{2.982778in}}%
+\pgfpathlineto{\pgfqpoint{0.631944in}{2.609321in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.631944in}{2.581543in}}{\pgfqpoint{0.659722in}{2.581543in}}%
+\pgfpathlineto{\pgfqpoint{0.659722in}{2.581543in}}%
 \pgfpathclose%
 \pgfusepath{stroke,fill}%
 \end{pgfscope}%
@@ -789,9 +683,9 @@
 \definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{0.925000in}{4.050389in}}%
-\pgfpathlineto{\pgfqpoint{1.063889in}{4.050389in}}%
-\pgfpathlineto{\pgfqpoint{1.202778in}{4.050389in}}%
+\pgfpathmoveto{\pgfqpoint{0.687500in}{2.906389in}}%
+\pgfpathlineto{\pgfqpoint{0.826389in}{2.906389in}}%
+\pgfpathlineto{\pgfqpoint{0.965278in}{2.906389in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -812,7 +706,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.063889in}{4.050389in}%
+\pgfsys@transformshift{0.826389in}{2.906389in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -820,7 +714,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.313889in,y=4.001778in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}booths algorithim}}%
+\pgftext[x=1.076389in,y=2.857778in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}booths algorithim}}%
 \end{pgfscope}%
 \begin{pgfscope}%
 \pgfsetbuttcap%
@@ -829,9 +723,9 @@
 \definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
-\pgfpathmoveto{\pgfqpoint{0.925000in}{3.856716in}}%
-\pgfpathlineto{\pgfqpoint{1.063889in}{3.856716in}}%
-\pgfpathlineto{\pgfqpoint{1.202778in}{3.856716in}}%
+\pgfpathmoveto{\pgfqpoint{0.687500in}{2.712716in}}%
+\pgfpathlineto{\pgfqpoint{0.826389in}{2.712716in}}%
+\pgfpathlineto{\pgfqpoint{0.965278in}{2.712716in}}%
 \pgfusepath{stroke}%
 \end{pgfscope}%
 \begin{pgfscope}%
@@ -852,7 +746,7 @@
 \pgfusepath{stroke,fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.063889in}{3.856716in}%
+\pgfsys@transformshift{0.826389in}{2.712716in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -860,7 +754,7 @@
 \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
 \pgfsetstrokecolor{textcolor}%
 \pgfsetfillcolor{textcolor}%
-\pgftext[x=1.313889in,y=3.808105in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}modified booths algorithim}}%
+\pgftext[x=1.076389in,y=2.664105in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}modified booths algorithim}}%
 \end{pgfscope}%
 \end{pgfpicture}%
 \makeatother%
diff --git a/report/report.aux b/report/report.aux
index 7be8ec5..452923f 100644
--- a/report/report.aux
+++ b/report/report.aux
@@ -1,3 +1,24 @@
 \relax 
-\@writefile{lol}{\contentsline {lstlisting}{../booth\textunderscore multiplier.py}{4}{}\protected@file@percent }
-\gdef \@abspage@last{10}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Add and Subtract operations of various Operand Lengths}}{4}{}\protected@file@percent }
+\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
+\newlabel{igraph}{{1}{4}{}{}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Add and Subtract operations of various Operand Lengths}}{5}{}\protected@file@percent }
+\newlabel{pgraph}{{2}{5}{}{}{}}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Number of additions and subtractions for various inputs}}{6}{}\protected@file@percent }
+\newlabel{speed_table}{{1}{6}{}{}{}}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Results of multiplication according to simulated multipliers}}{6}{}\protected@file@percent }
+\newlabel{result_table}{{2}{6}{}{}{}}
+\@writefile{lol}{\contentsline {lstlisting}{../booth\textunderscore multiplier.py}{7}{}\protected@file@percent }
+\gdef \LT@i {\LT@entry 
+    {1}{100.53595pt}\LT@entry 
+    {2}{96.636pt}\LT@entry 
+    {1}{101.87996pt}\LT@entry 
+    {1}{86.72392pt}\LT@entry 
+    {2}{168.636pt}\LT@entry 
+    {1}{80.62794pt}\LT@entry 
+    {1}{42.636pt}\LT@entry 
+    {1}{70.116pt}}
+\newlabel{RF1}{11}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Simulator self checking}}{11}{}\protected@file@percent }
+\newlabel{debug_table}{{3}{11}{}{}{}}
+\gdef \@abspage@last{11}
diff --git a/report/report.log b/report/report.log
index 1a52bc1..c65e108 100644
--- a/report/report.log
+++ b/report/report.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/Arch Linux) (preloaded format=pdflatex 2024.4.11)  12 APR 2024 14:03
+This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/Arch Linux) (preloaded format=pdflatex 2024.4.11)  12 APR 2024 15:40
 entering extended mode
  restricted \write18 enabled.
  %&-line parsing enabled.
@@ -153,25 +153,121 @@ Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1371.
 Package xcolor Info: Model `Gray' substituted by `gray' on input line 1372.
 Package xcolor Info: Model `wave' substituted by `hsb' on input line 1373.
 )
-(/usr/share/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty
-(/usr/share/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty
-(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex
-\pgfutil@everybye=\toks24
-\pgfutil@tempdima=\dimen166
-\pgfutil@tempdimb=\dimen167
-)
-(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def
-\pgfutil@abb=\box55
-)
-(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex
-(/usr/share/texmf-dist/tex/generic/pgf/pgf.revision.tex)
-Package: pgfrcs 2023-01-15 v3.1.10 (3.1.10)
-))
-Package: pgf 2023-01-15 v3.1.10 (3.1.10)
+(/usr/share/texmf-dist/tex/latex/caption/caption.sty
+Package: caption 2023/08/05 v3.6o Customizing captions (AR)
 
-(/usr/share/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty
-(/usr/share/texmf-dist/tex/latex/graphics/graphicx.sty
-Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR)
+(/usr/share/texmf-dist/tex/latex/caption/caption3.sty
+Package: caption3 2023/07/31 v2.4d caption3 kernel (AR)
+\caption@tempdima=\dimen166
+\captionmargin=\dimen167
+\caption@leftmargin=\dimen168
+\caption@rightmargin=\dimen169
+\caption@width=\dimen170
+\caption@indent=\dimen171
+\caption@parindent=\dimen172
+\caption@hangindent=\dimen173
+Package caption Info: Standard document class detected.
+)
+\c@caption@flags=\count278
+\c@continuedfloat=\count279
+Package caption Info: float package is loaded.
+Package caption Info: listings package is loaded.
+)
+(/usr/share/texmf-dist/tex/latex/caption/subcaption.sty
+Package: subcaption 2023/07/28 v1.6b Sub-captions (AR)
+Package caption Info: New subtype `subfigure' on input line 238.
+\c@subfigure=\count280
+Package caption Info: New subtype `subtable' on input line 238.
+\c@subtable=\count281
+)
+(/usr/share/texmf-dist/tex/latex/layouts/layouts.sty
+Package: layouts 2009/09/02 v2.6d graphical depiction of document elements
+\l@ylen=\skip53
+\layoutsbox=\box55
+\l@youtunitlength=\skip54
+\l@youtlinethick=\skip55
+\l@youtlinethickii=\skip56
+\l@ysetupparskip=\skip57
+\l@ysetupbaselineskip=\skip58
+\l@yonem=\skip59
+\l@yonex=\skip60
+\l@ylmarg=\skip61
+\l@yrmarg=\skip62
+\l@yitmindent=\skip63
+\l@ylblwidth=\skip64
+\l@ylblsep=\skip65
+\l@ylparindent=\skip66
+\l@ytsep=\skip67
+\l@ypskip=\skip68
+\l@yptsep=\skip69
+\l@ypsep=\skip70
+\l@yitmsep=\skip71
+\l@ytok=\toks24
+\l@youtpw=\count282
+\l@youtph=\count283
+\l@youthpi=\count284
+\l@youthpii=\count285
+\l@youthpiii=\count286
+\l@youthpiv=\count287
+\l@youthpv=\count288
+\l@youthpvi=\count289
+\l@youthpvii=\count290
+\l@youtparskip=\count291
+\l@youtvpi=\count292
+\l@youtvpii=\count293
+\l@youtvpiii=\count294
+\l@youtvpiv=\count295
+\l@youtvpv=\count296
+\l@youtvpvi=\count297
+\l@youtvpvii=\count298
+\l@youthdo=\count299
+\l@youthdi=\count300
+\l@youthdii=\count301
+\l@youthdiii=\count302
+\l@youthdiv=\count303
+\l@youthdv=\count304
+\l@youthdvi=\count305
+\l@youthdvii=\count306
+\l@youtvdo=\count307
+\l@youtvdi=\count308
+\l@youtvdii=\count309
+\l@youtvdiii=\count310
+\l@youtvdiv=\count311
+\l@youtvdv=\count312
+\l@youtvdvi=\count313
+\l@youtvdvii=\count314
+\l@youtvdviii=\count315
+\l@youtxci=\count316
+\l@youtxcii=\count317
+\l@youtxciii=\count318
+\l@youtxciv=\count319
+\l@youtxcv=\count320
+\l@youtxcvi=\count321
+\l@youtyci=\count322
+\l@youtycii=\count323
+\l@youtyciii=\count324
+\l@youtyciv=\count325
+\l@youtycv=\count326
+\l@youtycvi=\count327
+\l@youtycvii=\count328
+\l@youtycviii=\count329
+\l@youtxco=\count330
+\l@youtyco=\count331
+\l@ytempdima=\skip72
+\trimedge=\skip73
+\trimtop=\skip74
+\uppermargin=\skip75
+\spinemargin=\skip76
+)
+(/usr/share/texmf-dist/tex/latex/pdflscape/pdflscape.sty
+Package: pdflscape 2022-10-27 v0.13 Display of landscape pages in PDF
+
+(/usr/share/texmf-dist/tex/latex/pdflscape/pdflscape-nometadata.sty
+Package: pdflscape-nometadata 2022-10-28 v0.13 Display of landscape pages in PD
+F (HO)
+
+(/usr/share/texmf-dist/tex/latex/graphics/lscape.sty
+Package: lscape 2020/05/28 v3.02 Landscape Pages (DPC)
 
 (/usr/share/texmf-dist/tex/latex/graphics/graphics.sty
 Package: graphics 2022/03/10 v1.4e Standard LaTeX Graphics (DPC,SPQR)
@@ -183,42 +279,94 @@ Package: trig 2021/08/11 v1.11 sin cos tan (DPC)
 File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
 )
 Package graphics Info: Driver file: pdftex.def on input line 107.
+))
+Package pdflscape Info: Auto-detected driver: pdftex on input line 81.
+))
+(/usr/share/texmf-dist/tex/latex/graphics/rotating.sty
+Package: rotating 2016/08/11 v2.16d rotated objects in LaTeX
+
+(/usr/share/texmf-dist/tex/latex/graphics/graphicx.sty
+Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR)
+\Gin@req@height=\dimen174
+\Gin@req@width=\dimen175
+)
+(/usr/share/texmf-dist/tex/latex/base/ifthen.sty
+Package: ifthen 2022/04/13 v1.1d Standard LaTeX ifthen package (DPC)
+)
+\c@r@tfl@t=\count332
+\rotFPtop=\skip77
+\rotFPbot=\skip78
+\rot@float@box=\box56
+\rot@mess@toks=\toks25
+)
+(/usr/share/texmf-dist/tex/latex/tools/longtable.sty
+Package: longtable 2023-11-01 v4.19 Multi-page Table package (DPC)
+\LTleft=\skip79
+\LTright=\skip80
+\LTpre=\skip81
+\LTpost=\skip82
+\LTchunksize=\count333
+\LTcapwidth=\dimen176
+\LT@head=\box57
+\LT@firsthead=\box58
+\LT@foot=\box59
+\LT@lastfoot=\box60
+\LT@gbox=\box61
+\LT@cols=\count334
+\LT@rows=\count335
+\c@LT@tables=\count336
+\c@LT@chunks=\count337
+\LT@p@ftn=\toks26
 )
-\Gin@req@height=\dimen168
-\Gin@req@width=\dimen169
+(/usr/share/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty
+(/usr/share/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex
+\pgfutil@everybye=\toks27
+\pgfutil@tempdima=\dimen177
+\pgfutil@tempdimb=\dimen178
 )
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def
+\pgfutil@abb=\box62
+)
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex
+(/usr/share/texmf-dist/tex/generic/pgf/pgf.revision.tex)
+Package: pgfrcs 2023-01-15 v3.1.10 (3.1.10)
+))
+Package: pgf 2023-01-15 v3.1.10 (3.1.10)
+
+(/usr/share/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty
 (/usr/share/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty
 (/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex
 Package: pgfsys 2023-01-15 v3.1.10 (3.1.10)
 
 (/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex
-\pgfkeys@pathtoks=\toks25
-\pgfkeys@temptoks=\toks26
+\pgfkeys@pathtoks=\toks28
+\pgfkeys@temptoks=\toks29
 
 (/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.te
 x
-\pgfkeys@tmptoks=\toks27
+\pgfkeys@tmptoks=\toks30
 ))
-\pgf@x=\dimen170
-\pgf@y=\dimen171
-\pgf@xa=\dimen172
-\pgf@ya=\dimen173
-\pgf@xb=\dimen174
-\pgf@yb=\dimen175
-\pgf@xc=\dimen176
-\pgf@yc=\dimen177
-\pgf@xd=\dimen178
-\pgf@yd=\dimen179
+\pgf@x=\dimen179
+\pgf@y=\dimen180
+\pgf@xa=\dimen181
+\pgf@ya=\dimen182
+\pgf@xb=\dimen183
+\pgf@yb=\dimen184
+\pgf@xc=\dimen185
+\pgf@yc=\dimen186
+\pgf@xd=\dimen187
+\pgf@yd=\dimen188
 \w@pgf@writea=\write3
 \r@pgf@reada=\read2
-\c@pgf@counta=\count278
-\c@pgf@countb=\count279
-\c@pgf@countc=\count280
-\c@pgf@countd=\count281
-\t@pgf@toka=\toks28
-\t@pgf@tokb=\toks29
-\t@pgf@tokc=\toks30
-\pgf@sys@id@count=\count282
+\c@pgf@counta=\count338
+\c@pgf@countb=\count339
+\c@pgf@countc=\count340
+\c@pgf@countd=\count341
+\t@pgf@toka=\toks31
+\t@pgf@tokb=\toks32
+\t@pgf@tokc=\toks33
+\pgf@sys@id@count=\count342
  (/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg
 File: pgf.cfg 2023-01-15 v3.1.10 (3.1.10)
 )
@@ -232,8 +380,8 @@ File: pgfsys-common-pdf.def 2023-01-15 v3.1.10 (3.1.10)
 )))
 (/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex
 File: pgfsyssoftpath.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgfsyssoftpath@smallbuffer@items=\count283
-\pgfsyssoftpath@bigbuffer@items=\count284
+\pgfsyssoftpath@smallbuffer@items=\count343
+\pgfsyssoftpath@bigbuffer@items=\count344
 )
 (/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex
 File: pgfsysprotocol.code.tex 2023-01-15 v3.1.10 (3.1.10)
@@ -244,12 +392,12 @@ Package: pgfcore 2023-01-15 v3.1.10 (3.1.10)
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex)
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
-\pgfmath@dimen=\dimen180
-\pgfmath@count=\count285
-\pgfmath@box=\box56
-\pgfmath@toks=\toks31
-\pgfmath@stack@operand=\toks32
-\pgfmath@stack@operation=\toks33
+\pgfmath@dimen=\dimen189
+\pgfmath@count=\count345
+\pgfmath@box=\box63
+\pgfmath@toks=\toks34
+\pgfmath@stack@operand=\toks35
+\pgfmath@stack@operation=\toks36
 )
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex)
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex)
@@ -263,25 +411,25 @@ x) (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex)
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics
 .code.tex) (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex)
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex
-\c@pgfmathroundto@lastzeros=\count286
+\c@pgfmathroundto@lastzeros=\count346
 ))
 (/usr/share/texmf-dist/tex/generic/pgf/math/pgfint.code.tex)
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex
 File: pgfcorepoints.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgf@picminx=\dimen181
-\pgf@picmaxx=\dimen182
-\pgf@picminy=\dimen183
-\pgf@picmaxy=\dimen184
-\pgf@pathminx=\dimen185
-\pgf@pathmaxx=\dimen186
-\pgf@pathminy=\dimen187
-\pgf@pathmaxy=\dimen188
-\pgf@xx=\dimen189
-\pgf@xy=\dimen190
-\pgf@yx=\dimen191
-\pgf@yy=\dimen192
-\pgf@zx=\dimen193
-\pgf@zy=\dimen194
+\pgf@picminx=\dimen190
+\pgf@picmaxx=\dimen191
+\pgf@picminy=\dimen192
+\pgf@picmaxy=\dimen193
+\pgf@pathminx=\dimen194
+\pgf@pathmaxx=\dimen195
+\pgf@pathminy=\dimen196
+\pgf@pathmaxy=\dimen197
+\pgf@xx=\dimen198
+\pgf@xy=\dimen199
+\pgf@yx=\dimen256
+\pgf@yy=\dimen257
+\pgf@zx=\dimen258
+\pgf@zy=\dimen259
 LaTeX Font Info:    Trying to load font information for OT1+qpl on input line 9
 26.
 
@@ -290,30 +438,30 @@ File: ot1qpl.fd 2009/09/25 v1.2 font definition file for OT1/qpl
 ))
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex
 File: pgfcorepathconstruct.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgf@path@lastx=\dimen195
-\pgf@path@lasty=\dimen196
+\pgf@path@lastx=\dimen260
+\pgf@path@lasty=\dimen261
 ) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
 File: pgfcorepathusage.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgf@shorten@end@additional=\dimen197
-\pgf@shorten@start@additional=\dimen198
+\pgf@shorten@end@additional=\dimen262
+\pgf@shorten@start@additional=\dimen263
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex
 File: pgfcorescopes.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgfpic=\box57
-\pgf@hbox=\box58
-\pgf@layerbox@main=\box59
-\pgf@picture@serial@count=\count287
+\pgfpic=\box64
+\pgf@hbox=\box65
+\pgf@layerbox@main=\box66
+\pgf@picture@serial@count=\count347
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex
 File: pgfcoregraphicstate.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgflinewidth=\dimen199
+\pgflinewidth=\dimen264
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.t
 ex
 File: pgfcoretransformations.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgf@pt@x=\dimen256
-\pgf@pt@y=\dimen257
-\pgf@pt@temp=\dimen258
+\pgf@pt@x=\dimen265
+\pgf@pt@y=\dimen266
+\pgf@pt@temp=\dimen267
 ) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex
 File: pgfcorequick.code.tex 2023-01-15 v3.1.10 (3.1.10)
 )
@@ -325,20 +473,20 @@ x
 File: pgfcorepathprocessing.code.tex 2023-01-15 v3.1.10 (3.1.10)
 ) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex
 File: pgfcorearrows.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgfarrowsep=\dimen259
+\pgfarrowsep=\dimen268
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex
 File: pgfcoreshade.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgf@max=\dimen260
-\pgf@sys@shading@range@num=\count288
-\pgf@shadingcount=\count289
+\pgf@max=\dimen269
+\pgf@sys@shading@range@num=\count348
+\pgf@shadingcount=\count349
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex
 File: pgfcoreimage.code.tex 2023-01-15 v3.1.10 (3.1.10)
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex
 File: pgfcoreexternal.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgfexternal@startupbox=\box60
+\pgfexternal@startupbox=\box67
 )
 (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex
 File: pgfcorelayers.code.tex 2023-01-15 v3.1.10 (3.1.10)
@@ -353,40 +501,40 @@ File: pgfcorerdf.code.tex 2023-01-15 v3.1.10 (3.1.10)
 )))
 (/usr/share/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex
 File: pgfmoduleshapes.code.tex 2023-01-15 v3.1.10 (3.1.10)
-\pgfnodeparttextbox=\box61
+\pgfnodeparttextbox=\box68
 )
 (/usr/share/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex
 File: pgfmoduleplot.code.tex 2023-01-15 v3.1.10 (3.1.10)
 )
 (/usr/share/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty
 Package: pgfcomp-version-0-65 2023-01-15 v3.1.10 (3.1.10)
-\pgf@nodesepstart=\dimen261
-\pgf@nodesepend=\dimen262
+\pgf@nodesepstart=\dimen270
+\pgf@nodesepend=\dimen271
 )
 (/usr/share/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty
 Package: pgfcomp-version-1-18 2023-01-15 v3.1.10 (3.1.10)
 ))
 (/usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
 File: l3backend-pdftex.def 2024-02-20 L3 backend support: PDF output (pdfTeX)
-\l__color_backend_stack_int=\count290
-\l__pdf_internal_box=\box62
+\l__color_backend_stack_int=\count350
+\l__pdf_internal_box=\box69
 ) (./report.aux)
 \openout1 = `report.aux'.
 
-LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
-LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
-LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
-LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
-LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
-LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
-LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 34.
-LaTeX Font Info:    ... okay on input line 34.
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
+LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 40.
+LaTeX Font Info:    ... okay on input line 40.
 *geometry* driver: auto-detecting
 *geometry* detected driver: pdftex
 *geometry* verbose mode - [ preamble ] result:
@@ -421,20 +569,20 @@ LaTeX Font Info:    ... okay on input line 34.
 * \@reversemarginfalse
 * (1in=72.27pt=25.4mm, 1cm=28.453pt)
 
-\c@lstlisting=\count291
+\c@lstlisting=\count351
 (/usr/share/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
 [Loading MPS to PDF converter (version 2006.09.02).]
-\scratchcounter=\count292
-\scratchdimen=\dimen263
-\scratchbox=\box63
-\nofMPsegments=\count293
-\nofMParguments=\count294
-\everyMPshowfont=\toks34
-\MPscratchCnt=\count295
-\MPscratchDim=\dimen264
-\MPnumerator=\count296
-\makeMPintoPDFobject=\count297
-\everyMPtoPDFconversion=\toks35
+\scratchcounter=\count352
+\scratchdimen=\dimen272
+\scratchbox=\box70
+\nofMPsegments=\count353
+\nofMParguments=\count354
+\everyMPshowfont=\toks37
+\MPscratchCnt=\count355
+\MPscratchDim=\dimen273
+\MPnumerator=\count356
+\makeMPintoPDFobject=\count357
+\everyMPtoPDFconversion=\toks38
 ) (/usr/share/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
 Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
 Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
@@ -444,72 +592,84 @@ Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
 File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
 e
 ))
-LaTeX Font Info:    Trying to load font information for OT1+phv on input line 3
-5.
+Package caption Info: Begin \AtBeginDocument code.
+Package caption Info: longtable package is loaded.
+
+(/usr/share/texmf-dist/tex/latex/caption/ltcaption.sty
+Package: ltcaption 2021/01/08 v1.4c longtable captions (AR)
+)
+Package caption Info: rotating package is loaded.
+Package caption Info: End \AtBeginDocument code.
+
+
+Package layouts Warning: Layout scale set to 0.5 on input line 40.
 
+LaTeX Font Info:    Trying to load font information for OT1+phv on input line 4
+1.
 (/usr/share/texmf-dist/tex/latex/psnfss/ot1phv.fd
 File: ot1phv.fd 2020/03/25 scalable font definitions for OT1/phv.
 )
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <14.4> on input line 35.
+(Font)              <14.4> on input line 41.
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <7> on input line 35.
+(Font)              <7> on input line 41.
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <12> on input line 45.
+(Font)              <12> on input line 51.
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <8> on input line 45.
+(Font)              <8> on input line 51.
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <6> on input line 45.
+(Font)              <6> on input line 51.
  [1
 
 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}{/usr/share/texmf-dist/fonts
 /enc/dvips/base/8r.enc}{/usr/share/texmf-dist/fonts/enc/dvips/tex-gyre/q-rm.enc
 }]
-Underfull \hbox (badness 10000) in paragraph at lines 56--57
+Underfull \hbox (badness 10000) in paragraph at lines 62--63
 
  []
 
-[2] [3] (/usr/share/texmf-dist/tex/latex/listings/lstlang1.sty
-File: lstlang1.sty 2024/02/21 1.10 listings language file
-)
-(../booth_multiplier.py [4] [5] [6]) (./performance.pgf
+[2] (./iterations.pgf
 LaTeX Font Info:    External font `cmex10' loaded for size
 (Font)              <5> on input line 90.
-)
-Overfull \hbox (9.55966pt too wide) in paragraph at lines 865--124
- [] 
+) [3] (./performance.pgf) [4] [5] (./speed_table.tex)
+(./result_table.tex) [6] (/usr/share/texmf-dist/tex/latex/listings/lstlang1.sty
+File: lstlang1.sty 2024/02/21 1.10 listings language file
+) (../booth_multiplier.py [7] [8] [9]) (./debug_table.tex
+Overfull \hbox (47.28491pt too wide) in alignment at lines 1--5
+ [] [] [] [] [] [] [] [] 
  []
 
-(./iterations.pgf [7])
-Overfull \hbox (9.55966pt too wide) in paragraph at lines 834--125
- [][] 
+
+Overfull \hbox (47.28491pt too wide) in alignment at lines 5--24
+ [] [] [] [] [] [] [] [] 
  []
 
-(./speed_table.tex [8]) (./result_table.tex) [9] [10] (./report.aux)
+) [10] [11] (./report.aux)
  ***********
 LaTeX2e <2023-11-01> patch level 1
 L3 programming layer <2024-02-20>
  ***********
  ) 
 Here is how much of TeX's memory you used:
- 12527 strings out of 476076
- 233580 string characters out of 5793775
- 2448187 words of memory out of 5000000
- 34403 multiletter control sequences out of 15000+600000
- 592840 words of font info for 62 fonts, out of 8000000 for 9000
+ 14632 strings out of 476076
+ 272002 string characters out of 5793775
+ 2440187 words of memory out of 5000000
+ 36471 multiletter control sequences out of 15000+600000
+ 595618 words of font info for 63 fonts, out of 8000000 for 9000
  14 hyphenation exceptions out of 8191
- 87i,10n,93p,951b,1884s stack positions out of 10000i,1000n,20000p,200000b,200000s
+ 89i,10n,95p,951b,1887s stack positions out of 10000i,1000n,20000p,200000b,200000s
 </usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/t
 exmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texmf-dist/fonts
 /type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/
-amsfonts/cm/cmtt10.pfb></usr/share/texmf-dist/fonts/type1/public/tex-gyre/qplb.
-pfb></usr/share/texmf-dist/fonts/type1/public/tex-gyre/qplr.pfb></usr/share/tex
-mf-dist/fonts/type1/public/tex-gyre/qplri.pfb></usr/share/texmf-dist/fonts/type
-1/urw/helvetic/uhvr8a.pfb>
-Output written on report.pdf (10 pages, 224173 bytes).
+amsfonts/cm/cmtt10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cm
+tt12.pfb></usr/share/texmf-dist/fonts/type1/public/tex-gyre/qplb.pfb></usr/shar
+e/texmf-dist/fonts/type1/public/tex-gyre/qplr.pfb></usr/share/texmf-dist/fonts/
+type1/public/tex-gyre/qplri.pfb></usr/share/texmf-dist/fonts/type1/urw/helvetic
+/uhvr8a.pfb>
+Output written on report.pdf (11 pages, 233976 bytes).
 PDF statistics:
- 82 PDF objects out of 1000 (max. 8388607)
- 53 compressed objects within 1 object stream
+ 90 PDF objects out of 1000 (max. 8388607)
+ 58 compressed objects within 1 object stream
  0 named destinations out of 1000 (max. 500000)
  13 words of extra memory for PDF output out of 10000 (max. 10000000)
 
diff --git a/report/report.pdf b/report/report.pdf
index 69b779c..f0ce600 100644
--- a/report/report.pdf
+++ b/report/report.pdf
diff --git a/report/report.tex b/report/report.tex
index afa7680..23fc494 100644
--- a/report/report.tex
+++ b/report/report.tex
@@ -8,6 +8,12 @@
 \usepackage{float}
 \usepackage{listings}
 \usepackage{xcolor}
+\usepackage{caption}
+\usepackage{subcaption}
+\usepackage{layouts}
+\usepackage{pdflscape}
+\usepackage{rotating}
+\usepackage{longtable}
 
 \usepackage{pgf}
 
@@ -53,7 +59,19 @@ Bit 1 & Bit 0 & Action   \\
 \bottomrule
 \end{tabular}
 \end{table}
-After all iterations are complete, the result is arithmaticlly shifted once to the left, and the process repeats for the number of bits in an operand.\\
+After all iterations are complete, the result is arithmaticlly shifted once to the left, and the process repeats for the number of bits in an operand. The pseudo code for this algorithim is below:\\
+      \begin{verbatim}
+Booth:
+  result = multiplier << 1
+  loop (operand length) times:
+    if last two bits are 01:
+      result(upper half) += multiplicand
+    if last two bits are 10:
+      result(upper half) += twos_comp(multiplicand)
+    remove extra bits from result
+    arithmatic shift result right
+result >> 1
+      \end{verbatim}
 
 Modified booth's algorithim functions similar to Booth's algorithim, but checks the last \textit{three} bits instead. As such, there are a larger selection of actions for each iteration:
 \begin{table}[H]
@@ -74,17 +92,51 @@ Bit 2 & Bit 1 & Bit 0 & Action \\
 \end{tabular}
 \end{table}
 Because some operations require doubling the multiplicand, an extra bit is added to the most significant side of the workspace to avoid overflow. After each iteration, the result is arithmaticlly shifted right twice. The number of iterations is only half of the length of the operands. After all iterations, the workspace is shifted right once, and the second most significant bit is set to the first most significant bit as the result register does not include the extra bit.
+Pseudo code for this algorithim is listed below:
+\begin{verbatim}
+Modified booth:
+  multiplicand(MSB) = multiplicand(second MSB)
+  result = multiplier << 1
+  loop (operand length / 2) times:
+    if last two bits are 001 or 010:
+      result(upper half) += multiplicand
+    if last two bits are 011:
+      result(upper half) += multiplicand * 2
+    if last two bits are 100:
+      result(upper half) += twos_comp(multiplicand) * 2
+    if last two bits are 101 or 110:
+      result(upper half) += twos_comp(multiplicand)
+    remove extra bits from result
+    arithmatic shift result right twice
+  result >> 1
+  result(second MSB) = result(MSB)
+  result(MSB) = 0
+\end{verbatim}
+
 \par
 \section*{Simulation Implimentation}
 Both algorithims were simulated in Python in attempts to utalize its high level nature for rapid development. The table for Booth's algorithim was preformed with a simple if-then loop, while a switch case was used in modified booth's algorithim. Simple integers were used to represent registers. 
 \par
 One objective of this paper is to analyze and compare the peformance of these two algorithms for various operand lengths. As such, the length of operands had to be constantly accounted for. Aritmatic bitwise operations, including finding two's compliment, were all implimented using functions that took length as an input. Further more, extra bits were cleared after each iteration.
 \par
-To track down issues and test the validity of the multipliers, a debug function was written. To allow Python to natively work with the operands, each value is calculated from its two's compliment format. The converted numbers are then multiplied, and the result is compared to both Booth's Algorithim and Modified Booth's Algorithim. To ensure that the debugging function itself doesn't malfunction, all converted operands and expected results are put into a single large table for checking. The exported version of this table can be seen in table X. % TODO
+To track down issues and test the validity of the multipliers, a debug function was written. To allow Python to natively work with the operands, each value is calculated from its two's compliment format. The converted numbers are then multiplied, and the result is compared to both Booth's Algorithim and Modified Booth's Algorithim. To ensure that the debugging function itself doesn't malfunction, all converted operands and expected results are put into a single large table for checking. The exported version of this table can be seen on the last page, in table \ref{debug_table}. % TODO
 \section*{Analysis}
-Modified Booth's algorithim only requires half the iterations as Booth's algorithim. As such, it can be expected that the benifit of modified Booth's algorithim increases two fold with bit length. This can be shown by comparing the two curves in figure X. 
+Modified Booth's algorithim only requires half the iterations as Booth's algorithim. As such, it can be expected that the benifit of modified Booth's algorithim increases two fold with bit length. This can be shown by comparing the two curves in figure \ref{igraph}. 
+\begin{figure}[H]
+  \centering
+  \input{iterations.pgf}\\
+    \captionof{figure}{Add and Subtract operations of various Operand Lengths}
+    \label{igraph} 
+\end{figure}
+  
 \par
-Despite this, the nature of both algorithims dictate that modified booth's algorithim is not explicitly faster. Iteration count translates to the \textit{maxiumum} number of additions and subtractions. Figure X shows the performance of the two algorithims given different input lengths, while table x shows the actual data made to generate the plot. There are some interesting things to note. When operands contain repeating zeros or ones, both operations preform similarly, as only shifting is required. Operands containing entirely ones or zeros result in idential preformance. On the contrary, alternating bits within operands demonstrate where the two algorithims differ, as almost no bits can be skipped over. Operands made entirely of alternating bits result in the maximum performance diffrence, in which modified booth's algorithim is potentially two times faster.
+Despite this, the nature of both algorithims dictate that modified booth's algorithim is not explicitly faster. Iteration count translates to the \textit{maxiumum} number of additions and subtractions. Figure \ref{pgraph} shows the performance of the two algorithims given different input lengths, while table x shows the actual data made to generate the plot. There are some interesting things to note. When operands contain repeating zeros or ones, both operations preform similarly, as only shifting is required. Operands containing entirely ones or zeros result in idential preformance. On the contrary, alternating bits within operands demonstrate where the two algorithims differ, as almost no bits can be skipped over. Operands made entirely of alternating bits result in the maximum performance diffrence, in which modified booth's algorithim is potentially two times faster.
+\begin{figure}[H]
+  \centering
+    \input{performance.pgf}\\
+    \captionof{figure}{Add and Subtract operations of various Operand Lengths}
+    \label{pgraph} 
+\end{figure}
 \par
 All of this needs to be considered when designing an ALU. Modified booth's algorithim may improve speed, but requires substantially more hardware to impliment. One must consider if die space is to be allocated to optimize multiplication. In many applications, fast multiplication is unnessesary; many early single-chip processors and microcontrollers didn't impliment multiplication, as they were intended for simple embeded applications.
 \section*{Conclusion}
@@ -96,6 +148,21 @@ Hardware multipliers can help accellerate applications in which multiplication i
 \newpage
 \section*{Appendix}
 
+% efficiency gets comparitively better over length
+% not much for the smaller operands
+% lots of repeated 1s and 0s very good for both algorithims
+\begin{figure}[h]
+  \centering
+  \input{speed_table.tex}
+  \captionof{table}{Number of additions and subtractions for various inputs}
+  \label{speed_table}
+\end{figure}
+\begin{figure}[H]
+  \input{result_table.tex}
+  \captionof{table}{Results of multiplication according to simulated multipliers}
+  \label{result_table}
+\end{figure}
+
 \lstdefinestyle{mystyle}{
     backgroundcolor=\color{backcolour},
     commentstyle=\color{codegreen},
@@ -115,16 +182,17 @@ Hardware multipliers can help accellerate applications in which multiplication i
     tabsize=2
 }
 
+
 \lstset{style=mystyle}
+\newpage
+\subsection*{Code listing}
 \lstinputlisting[language=Python]{../booth_multiplier.py}
-% efficiency gets comparitively better over length
-% not much for the smaller operands
-% lots of repeated 1s and 0s very good for both algorithims
-\begin{center}
-  \input{performance.pgf}\\
-  \input{iterations.pgf}\\
-  \input{speed_table.tex}\\
-  \input{result_table.tex}\\
-\end{center}
-    
+\begin{sidewaysfigure}
+  \captionof{table}{Simulator self checking}
+  \label{debug_table}
+\input{debug_table.tex}
+\end{sidewaysfigure}
+
+
+
 \end{document}