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\author{{[}deleted{]}}
\pdfinfo{
  /Title (bit-manipulation.pdf)
  /Creator (Cheatography)
  /Author ({[}deleted{]})
  /Subject (Bit Manipulation Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Bit Manipulation Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{{[}deleted{]}} via \textcolor{DarkBackground}{\uline{cheatography.com/26304/cs/8563/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}{[}deleted{]} \\
  \uline{cheatography.com/deleted-26304} \\
  \end{tabulary}
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\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 6th July, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

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% 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)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}MSB: Most Significant Bit (left-most)} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`a,b`(lower case): a single bit} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`A,B`(upper case): set of bits, e.g. `A=\{a\_i\}, i={[}0,N-1{]}`} \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}{Bit-wise operators}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-lightbulb-o\}\} Bool/Bit analogy (helps to remember effect of operators): 1 is TRUE, 0 is FALSE} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-exclamation-triangle\}\} While Bool operators (`\&\&`, `||`, `!` - no equivalence for `\textasciitilde{}`) apply to simple TRUE/FALSE operands, bit-wise operators apply to {\bf{all}} bits of their operands (see {\emph{Example}} block)} \tn 
% Row Count 7 (+ 5)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\} `\&` (AND): both operands have 1s} \tn 
% Row Count 9 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\} `|` (OR): either or both operands have 1s} \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\} `\textasciicircum{}` (XOR, aka {\emph{exclusive OR}}): either {\bf{but not both}} operands have 1s} \tn 
% Row Count 13 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\} `\textasciitilde{}`(NOT, aka {\emph{complement}}): 1 becomes 0; 0 becomes 1} \tn 
% Row Count 15 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}  `\textless{}\textless{}` (left-shift): `a \textless{}\textless{} n` shifts all bits in `a` to the left by `n` positions and pads with 0s to the right.} \tn 
% Row Count 18 (+ 3)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}  `\textgreater{}\textgreater{}` (right-shift): `a \textgreater{}\textgreater{} n` shifts all bits in `a` to the right by `n` positions and pads with 0s to the left} \tn 
% Row Count 21 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{If `a` is an int, `a \textless{}\textless{} n` and `a \textgreater{}\textgreater{} n` are equivalent to multiplying an dividing respectively by `2\textasciicircum{}n\textasciicircum{}`}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{1-Bit Bit-wise Operators Summary}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nopainnogain_1467713486_Basic Operators - Summary.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Source: \seqsplit{https://www.hackerearth.com/notes/bit-manipulation/}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Examples (using `A = 1010; B = 1100`)}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`\&`: `A\&B = 1000`} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`|`: `A|B = 1110`} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`\textasciicircum{}`: `A\textasciicircum{}B = 0110`} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`\textasciitilde{}`: `\textasciitilde{}A = 11110101` (the number of 1′s depends on the type of `A`)} \tn 
% Row Count 5 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`\textless{}\textless{}`: `A \textless{}\textless{} 2 = 0000`} \tn 
% Row Count 6 (+ 1)
\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}{Usage}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Bit accessing: 1 \textless{}\textless{} 5 = 100000 TOREVIEW} \tn 
% Row Count 2 (+ 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}{Bit-wise Operators as Operations of Sets of Bits}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Using `ALL\_BIT` = 32/64 1s on a 32/64-bit machines} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Union: `A|B`} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Intersection: `A\&B`} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Subtraction: `A\&(\textasciitilde{}B)`} \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Negation: `ALL\_BITS\textasciicircum{}A`} \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Two's Complement (TsC)}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Most common number system to encode pos.a dn neg. numbers in a binary number representation of negative integers. One's complement is the alternative but seeimingly never used.} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}In TsC, MSB used for int sign (`-` for 1, `+` for 0)} \tn 
% Row Count 6 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Meaning 1: Mathematical operation on binary numbers (the {\emph{additive inverse}} op.)} \tn 
% Row Count 8 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Meaning 2: Binary signed number representation based on above mathematical operation, s.t. neg. numbers are represented byt hte TsC of the abs. value} \tn 
% Row Count 12 (+ 4)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}`N`-bit TsC range: `{[}-2\textasciicircum{}N-1\textasciicircum{}, +(2\textasciicircum{}N-1\textasciicircum{}-1){]}`} \tn 
% Row Count 14 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Conversion from TsC representation} \tn 
% Row Count 16 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{fa-caret-right\}\}Conversion to TsC representation} \tn 
% Row Count 17 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Source: \seqsplit{https://en.wikipedia.org/wiki/Two\%27s\_complement}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}