5.1a.2 Multiplexer

Multiplexer (MUX)

A multiplexer (MUX) is a digital switch that allows one of several input signals to be selected and passed through to a single output line. In a 2-input MUX with signals $A$ and $B$, and a selector bit $S$, the value of $S$ determines whether $A$ or $B$ is passed to the output. Specifically,
$\text{Out}=S\cdot B+\overline{S}\cdot A.$
The 2-input MUX is graphically represented as

\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}
 
   % Draw the multiplexer box
   \node at (0.5,0) {MUX};
   \draw[thick] (0,1) -- (0,-1) -- (1,-0.5) -- (1,0.5) -- cycle;
 
   % Draw the input lines
   \draw[thick, ->] (-1,0.5) -- (0,0.5) node[at start, left]{A};
   \draw[thick, ->] (-1,-0.5) -- (0,-0.5) node[at start, left]{B};
 
   % Draw the selector line
   \draw[thick, ->] (0.35,-1.6) -- (0.35,-0.8) node[at start, below]{S};
 
   % Draw the output line
   \draw[thick, ->] (1,0) -- (2,0) node[right]{Y};
 
\end{tikzpicture}
\end{document}

Understsanding

The easiest way to understand the MUX is using a truth table:

A	B	S	Out
0	0	0	0
1	0	0	1
0	0	1	0
1	0	1	0
0	1	0	0
1	1	0	1
0	1	1	1
1	1	1	1