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Multiplexer and Hexadecimal Numerals                                      [TOC]
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A __multiplexer__ is used to select from several inputs $a_0, \dots, a_m$ and
pass it through to the output. Selection is handled though a control signal. If
the control signal has $k$ bits you can select the output to be one of $m = 2^k$
inputs. So the number of inputs is always a power of two.

Technically a multiplexer can be build from scratch using logic gates. But for
convenience we will use the __builtin multiplexer that CircuitVerse provides__.

Together with a demultiplexer we will use this device for building an
integrated adder/subtractor. In this section the multiplexer is motivated by
building our own hex-diaplay from a seven-segment display.

Just using the opportunity we also introduce hexadecimal numerals for
representing bit pattern in a more compact and convenient form.

Assignment
==========
No explicit assignment for using CircuitVerse here. But of course you should
use the opportunity to make yourself familiar with the covered content.

However, there is __Assignment 2.2__ which is about binary and hexadecimal
numerals and representation of unsigned numbers.  This assignment can be done
with pencil and paper without computer aid. But of course, it makes sense to
use the circuit here (at least to check your results).

Video tutorial
==============

---- VIDEO ------------------------------
https://www.youtube.com/embed/3C5zUrSMPuA
-----------------------------------------


Some notes
==========


Representing bit pattern with hexadecimal numerals
--------------------------------------------------

Bit pattern consisting of a multiple of four bits can be represented in compact
form with hexadecimal digits. Write down the bit pattern in groups of $4$ and
apply the following replacement:

---- LATEX ---------------------------------------------------------------------
\begin{array}{lcllcllcllcl}
	0000 & \leadsto & 0 , &
\quad   0001 & \leadsto & 1 , &
\quad	0010 & \leadsto & 2 , &
\quad  	0011 & \leadsto & 3 , \\
    	0100 & \leadsto & 4 , &
\quad   0101 & \leadsto & 5 , &
\quad   0110 & \leadsto & 6 , &
\quad   0111 & \leadsto & 7 , \\
    	1000 & \leadsto & 8 , &
\quad  	1001 & \leadsto & 9 , &
\quad  	1010 & \leadsto & \text{A} , &
\quad  	1011 & \leadsto & \text{B} , \\
    	1100 & \leadsto & \text{C} , &
\quad 	1101 & \leadsto & \text{D} , &
\quad 	1110 & \leadsto & \text{E} , &
\quad 	1111 & \leadsto & \text{F}.  \\
\end{array}
--------------------------------------------------------------------------------

If it is necessary to point out that digits are hexadecimal we use the prefix
$0x$. For example, $\text{0xF8CA}$ is the bit pattern $\text{1111}$
$\text{1000}$ $\text{1100}$ $\text{1010}$. Whether uppercase or lowercase
letter are used for hexadecimal digits does not reason. For obvious reason the
Hex-Displays (like in CircuitVerse) are mixing upper and lower case usage.



:links: multiplexer -> https://en.wikipedia.org/wiki/Multiplexer
        builtin multiplexer that CircuitVerse provides -> https://docs.circuitverse.org/#/decodersandplexers?id=multiplexer
        Assignment 2.2 -> https://moodle.uni-ulm.de/mod/quiz/view.php?id=201436

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