\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{wayneswu}
\pdfinfo{
  /Title (do-not-use.pdf)
  /Creator (Cheatography)
  /Author (wayneswu)
  /Subject (do not use Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{A3A3A3}
\definecolor{LightBackground}{HTML}{F3F3F3}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\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{do not use Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{wayneswu} via \textcolor{DarkBackground}{\uline{cheatography.com/193768/cs/40338/}}}
\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}wayneswu \\
  \uline{cheatography.com/wayneswu} \\
  \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 18th September, 2023.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \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{tabularx}{17.67cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Positional Number System}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{17.67cm}}{- {\bf{Radix}} - number of unique symbols in a number system \newline % Row Count 2 (+ 2)
- usually 0-9, then A-Z% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Number System Base conversion}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{17.67cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/wayneswu_1694974813_AAA.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{2x vs 10y}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{17.67cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/wayneswu_1694975454_AAA.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{17.67cm}}{- Binary prefix are mainly use in memory capacity \newline - SI prefix are usually use in data transfer rate or storage space \newline  \newline - abbreviation * value = number of bits}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Binary Data Organization}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{17.67cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/wayneswu_1694974877_AAA.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{17.67cm}}{• a bit has 2 cells \newline  \newline • most significant (left) -{}-{}-{}-{}-{}- least significant (right) \newline • bit(b), byte(B) \newline  \newline • little endian - {\bf{top}} address to {\bf{bottom}} \newline • big endian - {\bf{bottom}} address to {\bf{top}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{x{7.2534 cm} x{10.0166 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Integer representation}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{UNSIGNED}} & {\bf{0 to (2\textasciicircum{}n\textasciicircum{})-1}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
normal & fill the rest with 0 (MSb) \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{SIGNED}} & {\bf{-(2\textasciicircum{}n-1\textasciicircum{}) to +(2\textasciicircum{}n-1\textasciicircum{})-1}} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
sign and magnitude & sign bit | positive int \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
1's complement (n-1's) & flip for negative int \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
2's complement (n's) & flip then + 1, for negative int \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{17.67cm}}{- {\bf{unsigned}} integers use {\bf{zero extension}} \newline - {\bf{signed}} integers use {\bf{sign extension}} \newline {\emph{in short, extend the MSb until you have reached the sufficient num of bits}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{integer operation overflow}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{17.67cm}}{{\bf{SHOULD \_\_\_; otherwise, overflow}} \newline % Row Count 1 (+ 1)
{\emph{ADDITION}} \newline % Row Count 2 (+ 1)
~~{\bf{UNSIGNED}} SHOULD NOT have carry \newline % Row Count 3 (+ 1)
~~{\bf{SIGNED {[}same sign{]}}} SHOULD remain the same sign \newline % Row Count 5 (+ 2)
~~{\bf{SIGNED {[}different sign{]}}} add using 2's complement representation (never overflow) \newline % Row Count 7 (+ 2)
{\emph{SUBTRACTION}} \newline % Row Count 8 (+ 1)
~~{\bf{UNSIGNED}} SHOULD HAVE carry \newline % Row Count 9 (+ 1)
~~{\bf{SIGNED}} A-B = A+B' (2's complement B)% Row Count 11 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{17.67cm}}{addition of signed integers {[}same sign{]} \newline ~~1. {\emph{first bit should never change}} \newline ~~2. {\emph{ignore carry if there is}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{x{5.2297 cm} x{4.5549 cm} x{7.0854 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{17.67cm}}{\bf\textcolor{white}{IEEE 754 Floating point for single precision}}  \tn
% Row 0
\SetRowColor{LightBackground}
1 - sign bit & 8 - exponent & 23 - mantissa \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
0 for positive & e' = e + 127 & f in 1.{\emph{f}} notation \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{17.67cm}}{{\bf{Example:}} \newline Given: 3.5₁₀ \newline ~~1. 3.5₁₀ = 11.1₂ \newline ~~2. 1.11 x 2\textasciicircum{}1\textasciicircum{} \newline ~~3. e' = 128₁₀ ==  1000\_0000₂ \newline ~~Answer: 1\_1000000\_110 0000...00000}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{x{5.3984 cm} x{5.3984 cm} x{6.0732 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{17.67cm}}{\bf\textcolor{white}{IEEE 754 Floating point for single precision}}  \tn
% Row 0
\SetRowColor{LightBackground}
1 - sign bit & 8 - exponent & 23 - mantissa \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{3}{x{17.67cm}}{0 for positive} \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{x{5.2297 cm} x{4.5549 cm} x{7.0854 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{17.67cm}}{\bf\textcolor{white}{test}}  \tn
% Row 0
\SetRowColor{LightBackground}
1 - sign bit & 8 - exponent & 23 - mantissa \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
0 for positive & e' = e + 127 & f in 1.{\emph{f}} notation \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{17.67cm}}{{\bf{Example:}} \newline Given: 3.5₁₀ \newline   1. 3.5₁₀ = 11.1₂ \newline   2. 1.11 x 21 \newline   3. e' = 128₁₀ == 1000\_0000₂ \newline   Answer: 1\_1000000\_110 0000...00000}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{17.67cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Special cases floating single precision}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{17.67cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/wayneswu_1695011335_AAA.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}



\end{document}