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%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
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% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
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\usepackage{MnSymbol}           % Symbols
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% Document Info
\author{{[}deleted{]}}
\pdfinfo{
  /Title (signed-number-binary-representation.pdf)
  /Creator (Cheatography)
  /Author ({[}deleted{]})
  /Subject (Signed Number Binary Representation Cheat Sheet)
}

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% Header and Footer
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\fancyhead{} % Set header to blank
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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Signed Number Binary Representation Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{{[}deleted{]}} via \textcolor{DarkBackground}{\uline{cheatography.com/26304/cs/8570/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}{[}deleted{]} \\
  \uline{cheatography.com/deleted-26304} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 8th July, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Abbreviations and Notations}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}LSB: Least Significant Bit (right-most bit)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}MSB: Most Significant Bit (left-most bit)} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}SaM: Sign-and-Magnitude representation} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}OsC: One's Complement representation} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}TsC: Two's Complement representation} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`b`: a single bit} \tn 
% Row Count 11 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`B\_x`: set of bits representing number `x` base `10`, i.e. `B\_x=\{b\_i\}, i={[}0,N-1{]}`. \{\{fa-search\}\}: in a 4-bit register, `B\_x=0101` for `x=5`} \tn 
% Row Count 15 (+ 4)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Unless specified otherwise, we will use throughout 8-bit (1 byte) registers to represent integers =\textgreater{} ranges are `{[}0,255{]}` for unsigned `int`s and `{[}-127, 127{]}` for signed `int`s.} \tn 
% Row Count 19 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Types of Number representation}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Mainly: SaM, OsC, TsC, excess-`K`, Base-`2`} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}TsC most widely used. Here, only SaM, OsC and TsC are coverved.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}For SaM/OsC/TsC, `B\_x` for `x\textgreater{}0` is the same for all representations (this is not the case for excess-`K` and Base-`2`) `=\textgreater{}` half the full range is always `B\_{[}0, 127{]}={[}00000000, 01111111{]}`.} \tn 
% Row Count 9 (+ 5)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`-x` will then depend on choice of representation.} \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{SaM}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-book\}\} MSB directly represents the sign. `0` is for positive integers, `1` is for negative integers. Remaining bits are for magnitude} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-search\}\}: `x = 43` has `B\_x = 00101011` =\textgreater{} `x = -43` has `B\_x = 10101011`} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-exclamation-triangle\}\}2 representations for `0` (`00000000` (`0`) and `10000000` (`−0`))} \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{OsC}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-book\}\} For `x\textgreater{}0`, {\bf{`-x` represented by `B\_(-x) = \textasciitilde{}B\_x`}}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-search\}\}`x = 43` has `B\_x = 00101011` =\textgreater{} `x = -43` has `B\_x = 11010100`} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-exclamation-triangle\}\}2 representations for `0` (`B\_0 = 00000000` and `B\_(-0) = \textasciitilde{}B\_0 = 11111111`). In fact `B\_x + B\_(-x) = B\_(-0)`} \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-exclamation-triangle\}\}{\bf{Sometimes}} imposes and end-around carry/borrow in addition/subtraction (in a `4`-bit register, try `7-3`, {\bf{`7+(-3)`}}, `(-7)+3`, {\bf{`3-7`}}, with corresponding OsC bit representation). {\bf{These do not occur in TsC arithmetic}}} \tn 
% Row Count 13 (+ 6)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-info\}\} For `x\textgreater{}0` with representation `B\_x`, `B\_(-x) = \textasciitilde{}B\_x` as per OsC definition `\textless{}=\textgreater{} B\_(-x) = \textasciitilde{}B\_0 - B\_x`} \tn 
% Row Count 16 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{References}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}\{\{link="https://en.wikipedia.org/wiki/Signed\_number\_representations"\}\}Signed number Representation: Wikipedia\{\{/popup\}\}} \tn 
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% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}\{\{link="https://en.wikipedia.org/wiki/Two\%27s\_complement"\}\}Two's complement: Wikipedia\{\{/popup\}\}} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}\{\{link="https://www.youtube.com/watch?v=S9LJknZTyos"\}\}Binary subtraction: YouTube\{\{/link\}\}} \tn 
% Row Count 9 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}