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\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
%\usepackage[brazil]{babel}
\usepackage{palatino}
\usepackage{fullpage}
\usepackage{hyperref}
 
\usepackage{multicol}
\usepackage{graphicx}
\usepackage{float}
\usepackage{moreverb}
\usepackage{verbatim}
 
\usepackage{multirow}
 
\title{\textbf{AMI and HDB1 Line Codes - VHDL Implementation.}}
\author{Ribamar Santarosa, ribamar@gmail.com}
\date{Outubro/Novembro 2006.}
 
\begin{document}
\maketitle
 
 
\begin{abstract}
Line codings are methods for coding digital data for making them
less susceptible to signal losses during transmission. This project
implements the AMI --- Alternate Mark Inverse --- and HDB1 --- High
Density Bipolar of order 1 codings. This file documents their
implementation.
\end{abstract}
 
\section{Specification.}
 
 
\paragraph{AMI.} This coding takes a binary sequency into a
ternary sequency having the signals 0, +1, -1 by the following way:
 
\begin{itemize}
\item Inputs of 1 are coded as +1 or -1 alternately.
\item Inputs of 0 are coded always as 0.
\end{itemize}
 
Example:
\begin{verbatim}
Input
 1 0  1 0  1  1 0 0 0  1 0  1  1 0 0  1 0  1 0 0 0  1  1  1
Output
+1 0 -1 0 +1 -1 0 0 0 +1 0 -1 +1 0 0 -1 0 +1 0 0 0 -1 +1 -1
\end{verbatim}
 
\paragraph{HDB1.} This coding takes a binary sequency into a
ternary sequency having the signals 0, +1, -1 by the following way:
 
\begin{itemize}
\item Inputs of 1 are coded as either +1 or -1.
\item Paired inputs of 0 are coded as either +1+1 or -1-1.
\item Isolated inputs of 0, ie, inputs of 0 not followed by 1 which
weren't paired to another 0 (thus forming +1+1 or -1-1) are coded
as 0.
\item Outputs have always alternate signals. If the last output was
-1 and the input is 00, the next output is coded as +1+1, if the
last output was -1-1 and the input is 1, the next output is +1.
\end{itemize}
 
Example:
\begin{verbatim}
Input
 1 0  1 0  1  1  0  0 0  1 0  1  1  0  0  1 0  1  0  0  0  0  1  1
Output
+1 0 -1 0 +1 -1 +1 +1 0 -1 0 +1 -1 +1 +1 -1 0 +1 -1 -1 +1 +1 -1 +1
\end{verbatim}
 
 
 
%\begin{multicols}{2}
 
\section{AMI Encoder. }
 
\begin{figure}[H]
\centering
\includegraphics[scale=0.35]{estados-ami_enc}
\caption[ ]{\label{estados-ami_enc} State Map.  }
\end{figure}
 
\begin{multicols}{2}
Truth Table: \\
 
\begin{tabular}{|c|c|cc|c|}
\hline
$q$ & $e$ & $S_0$ & $ S_1$ & $q^+$ \\
\hline
 
 
\hline
1 & 0 & 0 & 0 & 1 \\
1 & 1 & 0 & 1 & 0 \\
\hline
\end{tabular}
 
Karnaugh Map isn't necessary: \\
$ S_0 = e \cdot q'$ \\
$ S_1 = e \cdot q $ \\
$ q^+ = e \oplus q$ \\
 
\end{multicols}
 
%\hrule
 
\section{AMI Decoder. }
\begin{multicols}{2}
 
 
\begin{figure}[H]
\centering
\includegraphics[scale=0.35]{estados-ami_dec}
\caption[ ]{\label{estados-ami_dec} State Map. }
\end{figure}
 
 
Truth Table:
 
\begin{tabular}{|cc|c|}
\hline
$e_0$ & $e_1$ & $S$  \\
\hline
 
 
1 & 0 & 1 \\
1 & 1 & $X$ \\
\hline
\end{tabular}
 
\vspace{50pt}
Karnaugh Map isn't necessary: \\
$ S = e_0 + e_1 $ \\
 
\end{multicols}
%\hrule
 
 
\section{HDB1 Encoder. }
\begin{figure}[H]
\centering
\includegraphics[scale=0.35]{estados-hdb1_enc}
\caption[ ]{\label{estados-hdb1_enc} State Map. }
\end{figure}
 
 
\begin{multicols}{2}
 
 
Truth Table: \\
 ~\\
\begin{tabular}{|cccc|ccc|cc|}
\hline
$E$ & $q_0$ & $q_1$ & $q_2$ & $q_0^+$ & $q_1^+$ & $q_2^+$ & $S_0$ & $S_1$ \\
\hline
$0$ & $0$ & $0$ & $0$ &    $0$ & $0$ & $1$ &    $1$ & $0$  \\
$1$ & $0$ & $0$ & $0$ &    $1$ & $1$ & $0$ &    $1$ & $0$  \\
\hline
$0$ & $0$ & $0$ & $1$ &    $0$ & $1$ & $0$ &    $0$ & $1$  \\
$1$ & $0$ & $0$ & $1$ &    $1$ & $1$ & $0$ &    $0$ & $0$  \\
\hline
$0$ & $0$ & $1$ & $0$ &    $0$ & $1$ & $1$ &    $0$ & $1$  \\
$1$ & $0$ & $1$ & $0$ &    $0$ & $0$ & $0$ &    $0$ & $1$  \\
\hline
$0$ & $0$ & $1$ & $1$ &    $1$ & $0$ & $0$ &    $1$ & $0$  \\
$1$ & $0$ & $1$ & $1$ &    $0$ & $0$ & $0$ &    $0$ & $0$  \\
\hline
$0$ & $1$ & $0$ & $0$ &    $0$ & $0$ & $1$ &    $1$ & $0$  \\
$1$ & $1$ & $0$ & $0$ &    $1$ & $1$ & $0$ &    $1$ & $0$  \\
\hline
$$X$$ & $1$ & $0$ & $1$ &    $$X$$ & $$X$$ & $$X$$ &    $$X$$ & $$X$$  \\
\hline
$0$ & $1$ & $1$ & $0$ &    $1$ & $1$ & $1$ &    $0$ & $1$  \\
$1$ & $1$ & $1$ & $0$ &    $0$ & $0$ & $0$ &    $0$ & $1$  \\
\hline
$0$ & $1$ & $1$ & $1$ &    $0$ & $0$ & $0$ &    $1$ & $0$  \\
$1$ & $1$ & $1$ & $1$ &    $0$ & $0$ & $0$ &    $0$ & $1$  \\
\hline
\end{tabular}
 
$q_0^+$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$E q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} &   &   & 1 & 1 \\
$q_1 q_2$  & \tiny{$01$} &   & $X$ & $X$ & 1 \\
           & \tiny{$11$} & 1 &   &   &   \\
           & \tiny{$10$} &   & 1 &   &   \\
\hline
\end{tabular}
 
$q_0^+ = E . q_1' + E'.q_0'.q_1.q_2 + E'.q_0.q_1 . q_2' $
 
$q_1^+$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$E q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} &   &   & 1 & 1 \\
$q_1 q_2$  & \tiny{$01$} & 1 & $X$ & $X$ & 1 \\
           & \tiny{$11$} &   &   &   &   \\
           & \tiny{$10$} & 1 & 1 &   &   \\
\hline
\end{tabular}
 
$q_1^+ = E . q_1' + q_1'.q_2 + E'.q_1.q_2' $
 
$q_2^+$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$E q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} & 1 & 1 &   &   \\
$q_1 q_2$  & \tiny{$01$} &   & $X$ & $X$ &   \\
           & \tiny{$11$} &   &   &   &   \\
           & \tiny{$10$} & 1 & 1 &   &   \\
\hline
\end{tabular}
 
$q_2^+ = E'. q_2'$
 
$S_0$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$E q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} & 1 & 1 & 1 & 1 \\
$q_1 q_2$  & \tiny{$01$} &   & $X$ & $X$ &   \\
           & \tiny{$11$} & 1 & 1 &   &   \\
           & \tiny{$10$} &   &   &   &   \\
\hline
\end{tabular}
 
$S_0 = q_1'. q_2' + E'.q_1. q_2 $
 
$S_1$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$E q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} &   &   &   &   \\
$q_1 q_2$  & \tiny{$01$} & 1 & $X$ & $X$ &   \\
           & \tiny{$11$} &   &   &   &   \\
           & \tiny{$10$} & 1 & 1 & 1 & 1 \\
\hline
\end{tabular}
 
$S_1 = q_1. q_2' + E'.q_1'. q_2 $
 
 
\end{multicols}
 
\vspace{10pt}
%\hrule
 
\section{HDB1 Decoder. }
 
\begin{figure}[H]
\centering
\includegraphics[scale=0.2665]{estados-hdb1_dec}
\caption[ ]{\label{estados-hdb1_dec} State Map. }
\end{figure}
 
 
\begin{multicols}{2}
 
Truth Table:
\begin{tabular}{|cc|cc|cc|c|}
\hline
$e_1$ & $e_0$ & $q_1$ & $q_0$ & $q^+_0$ & $q^+_1$ & $S$ \\
\hline
 
 
 
 
\hline
 
 
 
 
\hline
1 & 0 & 0 & 0   & 0 & 1 & 0 \\
1 & 0 & 0 & 1   & 1 & 0 & 1 \\
1 & 0 & 1 & 0   & 0 & 0 & 0 \\
1 & 0 & 1 & 1   & $X$ & $X$ & $X$ \\
\hline
1 & 1 & 0 & 0   & $X$ & $X$ & $X$ \\
1 & 1 & 0 & 1   & $X$ & $X$ & $X$ \\
1 & 1 & 1 & 0   & $X$ & $X$ & $X$ \\
1 & 1 & 1 & 1   & $X$ & $X$ & $X$ \\
\hline
\end{tabular}
 
$q0$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$q_1 q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} &   &   & $X$ &   \\
$e_0 e_1$  & \tiny{$01$} &   &   & $X$ &   \\
           & \tiny{$11$} & $X$ & $X$ & $X$ & $X$ \\
           & \tiny{$10$} &   & 1 & $X$ &   \\
\hline
\end{tabular}
 
$q_0^+ = q_0'. e_0$
 
$q1$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$q_1 q_0$ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} &   &   & $X$ &   \\
$e_0 e_1$  & \tiny{$01$} & 1 &   & $X$ & 1 \\
           & \tiny{$11$} & $X$ & $X$ & $X$ & $X$ \\
           & \tiny{$10$} & 1 &   & $X$ &   \\
\hline
\end{tabular}
 
 
$q_1^+ = q_1'. e_1$
 
$S$:
\begin{tabular}{|cc|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{$q_1 q_0 $ } \\
           & & \tiny{$00$} & \tiny{$01$}  & \tiny{$11$}  & \tiny{$10$}  \\
           & \tiny{$00$} &   & 1 & $X$ & 1 \\
$e_1 e_2$  & \tiny{$01$} &   &   & $X$ & 1 \\
           & \tiny{$11$} & $X$ & $X$ & $X$ & $X$ \\
           & \tiny{$10$} &   & 1 & $X$ &   \\
\hline
\end{tabular}
 
$ S = q_0. e_0' + q_1. e_1' $
 
 
\vspace{10pt}
 
\end{multicols}
 
%\hrule
 
 
\end{document}
 

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Subversion Repositories line_codes

[/] [line_codes/] [trunk/] [doc/] [src/] [documentation.tex] - Blame information for rev 8

Line No.	Rev	Author	Line
1	3	ribamar	`\documentclass[11pt]{article}`
2			`\usepackage[utf8]{inputenc}`
3			`%\usepackage[brazil]{babel}`
4			`\usepackage{palatino}`
5			`\usepackage{fullpage}`
6			`\usepackage{hyperref}`
7
8			`\usepackage{multicol}`
9			`\usepackage{graphicx}`
10			`\usepackage{float}`
11			`\usepackage{moreverb}`
12			`\usepackage{verbatim}`
13
14			`\usepackage{multirow}`
15
16			`\title{\textbf{AMI and HDB1 Line Codes - VHDL Implementation.}}`
17			`\author{Ribamar Santarosa, ribamar@gmail.com}`
18			`\date{Outubro/Novembro 2006.}`
19
20			`\begin{document}`
21			`\maketitle`
22
23
24			`\begin{abstract}`
25			`Line codings are methods for coding digital data for making them`
26			`less susceptible to signal losses during transmission. This project`
27			`implements the AMI --- Alternate Mark Inverse --- and HDB1 --- High`
28			`Density Bipolar of order 1 codings. This file documents their`
29			`implementation.`
30			`\end{abstract}`
31
32			`\section{Specification.}`
33
34
35			`\paragraph{AMI.} This coding takes a binary sequency into a`
36			`ternary sequency having the signals 0, +1, -1 by the following way:`
37
38			`\begin{itemize}`
39			`\item Inputs of 1 are coded as +1 or -1 alternately.`
40			`\item Inputs of 0 are coded always as 0.`
41			`\end{itemize}`
42
43			`Example:`
44			`\begin{verbatim}`
45			`Input`
46			`1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1`
47			`Output`
48			`+1 0 -1 0 +1 -1 0 0 0 +1 0 -1 +1 0 0 -1 0 +1 0 0 0 -1 +1 -1`
49			`\end{verbatim}`
50
51			`\paragraph{HDB1.} This coding takes a binary sequency into a`
52			`ternary sequency having the signals 0, +1, -1 by the following way:`
53
54			`\begin{itemize}`
55			`\item Inputs of 1 are coded as either +1 or -1.`
56			`\item Paired inputs of 0 are coded as either +1+1 or -1-1.`
57			`\item Isolated inputs of 0, ie, inputs of 0 not followed by 1 which`
58			`weren't paired to another 0 (thus forming +1+1 or -1-1) are coded`
59			`as 0.`
60			`\item Outputs have always alternate signals. If the last output was`
61			`-1 and the input is 00, the next output is coded as +1+1, if the`
62			`last output was -1-1 and the input is 1, the next output is +1.`
63			`\end{itemize}`
64
65			`Example:`
66			`\begin{verbatim}`
67			`Input`
68			`1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1`
69			`Output`
70			`+1 0 -1 0 +1 -1 +1 +1 0 -1 0 +1 -1 +1 +1 -1 0 +1 -1 -1 +1 +1 -1 +1`
71			`\end{verbatim}`
72
73
74
75			`%\begin{multicols}{2}`
76
77			`\section{AMI Encoder. }`
78
79			`\begin{figure}[H]`
80			`\centering`
81			`\includegraphics[scale=0.35]{estados-ami_enc}`
82			`\caption[ ]{\label{estados-ami_enc} State Map. }`
83			`\end{figure}`
84
85			`\begin{multicols}{2}`
86			`Truth Table: \\`
87
88			`\begin{tabular}{\|c\|c\|cc\|c\|}`
89			`\hline`
90			`$q$ & $e$ & $S_0$ & $ S_1$ & $q^+$ \\`
91			`\hline`
92
93
94			`\hline`
95			`1 & 0 & 0 & 0 & 1 \\`
96			`1 & 1 & 0 & 1 & 0 \\`
97			`\hline`
98			`\end{tabular}`
99
100			`Karnaugh Map isn't necessary: \\`
101			`$ S_0 = e \cdot q'$ \\`
102			`$ S_1 = e \cdot q $ \\`
103			`$ q^+ = e \oplus q$ \\`
104
105			`\end{multicols}`
106
107			`%\hrule`
108
109			`\section{AMI Decoder. }`
110			`\begin{multicols}{2}`
111
112
113			`\begin{figure}[H]`
114			`\centering`
115			`\includegraphics[scale=0.35]{estados-ami_dec}`
116			`\caption[ ]{\label{estados-ami_dec} State Map. }`
117			`\end{figure}`
118
119
120			`Truth Table:`
121
122			`\begin{tabular}{\|cc\|c\|}`
123			`\hline`
124			`$e_0$ & $e_1$ & $S$ \\`
125			`\hline`
126
127
128			`1 & 0 & 1 \\`
129			`1 & 1 & $X$ \\`
130			`\hline`
131			`\end{tabular}`
132
133			`\vspace{50pt}`
134			`Karnaugh Map isn't necessary: \\`
135			`$ S = e_0 + e_1 $ \\`
136
137			`\end{multicols}`
138			`%\hrule`
139
140
141			`\section{HDB1 Encoder. }`
142			`\begin{figure}[H]`
143			`\centering`
144			`\includegraphics[scale=0.35]{estados-hdb1_enc}`
145			`\caption[ ]{\label{estados-hdb1_enc} State Map. }`
146			`\end{figure}`
147
148
149			`\begin{multicols}{2}`
150
151
152			`Truth Table: \\`
153			`~\\`
154			`\begin{tabular}{\|cccc\|ccc\|cc\|}`
155			`\hline`
156			`$E$ & $q_0$ & $q_1$ & $q_2$ & $q_0^+$ & $q_1^+$ & $q_2^+$ & $S_0$ & $S_1$ \\`
157			`\hline`
158			`$0$ & $0$ & $0$ & $0$ & $0$ & $0$ & $1$ & $1$ & $0$ \\`
159			`$1$ & $0$ & $0$ & $0$ & $1$ & $1$ & $0$ & $1$ & $0$ \\`
160			`\hline`
161			`$0$ & $0$ & $0$ & $1$ & $0$ & $1$ & $0$ & $0$ & $1$ \\`
162			`$1$ & $0$ & $0$ & $1$ & $1$ & $1$ & $0$ & $0$ & $0$ \\`
163			`\hline`
164			`$0$ & $0$ & $1$ & $0$ & $0$ & $1$ & $1$ & $0$ & $1$ \\`
165			`$1$ & $0$ & $1$ & $0$ & $0$ & $0$ & $0$ & $0$ & $1$ \\`
166			`\hline`
167			`$0$ & $0$ & $1$ & $1$ & $1$ & $0$ & $0$ & $1$ & $0$ \\`
168			`$1$ & $0$ & $1$ & $1$ & $0$ & $0$ & $0$ & $0$ & $0$ \\`
169			`\hline`
170			`$0$ & $1$ & $0$ & $0$ & $0$ & $0$ & $1$ & $1$ & $0$ \\`
171			`$1$ & $1$ & $0$ & $0$ & $1$ & $1$ & $0$ & $1$ & $0$ \\`
172			`\hline`
173			`$$X$$ & $1$ & $0$ & $1$ & $$X$$ & $$X$$ & $$X$$ & $$X$$ & $$X$$ \\`
174			`\hline`
175			`$0$ & $1$ & $1$ & $0$ & $1$ & $1$ & $1$ & $0$ & $1$ \\`
176			`$1$ & $1$ & $1$ & $0$ & $0$ & $0$ & $0$ & $0$ & $1$ \\`
177			`\hline`
178			`$0$ & $1$ & $1$ & $1$ & $0$ & $0$ & $0$ & $1$ & $0$ \\`
179			`$1$ & $1$ & $1$ & $1$ & $0$ & $0$ & $0$ & $0$ & $1$ \\`
180			`\hline`
181			`\end{tabular}`
182
183			`$q_0^+$:`
184			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
185			`\hline`
186			`\multicolumn{6}{\|c\|}{$E q_0$ } \\`
187			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
188			`& \tiny{$00$} & & & 1 & 1 \\`
189			`$q_1 q_2$ & \tiny{$01$} & & $X$ & $X$ & 1 \\`
190			`& \tiny{$11$} & 1 & & & \\`
191			`& \tiny{$10$} & & 1 & & \\`
192			`\hline`
193			`\end{tabular}`
194
195			$q_0^+ = E . q_1' + E'.q_0'.q_1.q_2 + E'.q_0.q_1 . q_2' $
196
197			`$q_1^+$:`
198			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
199			`\hline`
200			`\multicolumn{6}{\|c\|}{$E q_0$ } \\`
201			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
202			`& \tiny{$00$} & & & 1 & 1 \\`
203			`$q_1 q_2$ & \tiny{$01$} & 1 & $X$ & $X$ & 1 \\`
204			`& \tiny{$11$} & & & & \\`
205			`& \tiny{$10$} & 1 & 1 & & \\`
206			`\hline`
207			`\end{tabular}`
208
209			$q_1^+ = E . q_1' + q_1'.q_2 + E'.q_1.q_2' $
210
211			`$q_2^+$:`
212			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
213			`\hline`
214			`\multicolumn{6}{\|c\|}{$E q_0$ } \\`
215			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
216			`& \tiny{$00$} & 1 & 1 & & \\`
217			`$q_1 q_2$ & \tiny{$01$} & & $X$ & $X$ & \\`
218			`& \tiny{$11$} & & & & \\`
219			`& \tiny{$10$} & 1 & 1 & & \\`
220			`\hline`
221			`\end{tabular}`
222
223			$q_2^+ = E'. q_2'$
224
225			`$S_0$:`
226			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
227			`\hline`
228			`\multicolumn{6}{\|c\|}{$E q_0$ } \\`
229			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
230			`& \tiny{$00$} & 1 & 1 & 1 & 1 \\`
231			`$q_1 q_2$ & \tiny{$01$} & & $X$ & $X$ & \\`
232			`& \tiny{$11$} & 1 & 1 & & \\`
233			`& \tiny{$10$} & & & & \\`
234			`\hline`
235			`\end{tabular}`
236
237			$S_0 = q_1'. q_2' + E'.q_1. q_2 $
238
239			`$S_1$:`
240			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
241			`\hline`
242			`\multicolumn{6}{\|c\|}{$E q_0$ } \\`
243			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
244			`& \tiny{$00$} & & & & \\`
245			`$q_1 q_2$ & \tiny{$01$} & 1 & $X$ & $X$ & \\`
246			`& \tiny{$11$} & & & & \\`
247			`& \tiny{$10$} & 1 & 1 & 1 & 1 \\`
248			`\hline`
249			`\end{tabular}`
250
251			$S_1 = q_1. q_2' + E'.q_1'. q_2 $
252
253
254			`\end{multicols}`
255
256			`\vspace{10pt}`
257			`%\hrule`
258	6	ribamar
259	3	ribamar	`\section{HDB1 Decoder. }`
260
261			`\begin{figure}[H]`
262			`\centering`
263			`\includegraphics[scale=0.2665]{estados-hdb1_dec}`
264			`\caption[ ]{\label{estados-hdb1_dec} State Map. }`
265			`\end{figure}`
266
267
268			`\begin{multicols}{2}`
269
270			`Truth Table:`
271			`\begin{tabular}{\|cc\|cc\|cc\|c\|}`
272			`\hline`
273			`$e_1$ & $e_0$ & $q_1$ & $q_0$ & $q^+_0$ & $q^+_1$ & $S$ \\`
274			`\hline`
275
276
277
278
279			`\hline`
280
281
282
283
284			`\hline`
285			`1 & 0 & 0 & 0 & 0 & 1 & 0 \\`
286			`1 & 0 & 0 & 1 & 1 & 0 & 1 \\`
287			`1 & 0 & 1 & 0 & 0 & 0 & 0 \\`
288			`1 & 0 & 1 & 1 & $X$ & $X$ & $X$ \\`
289			`\hline`
290			`1 & 1 & 0 & 0 & $X$ & $X$ & $X$ \\`
291			`1 & 1 & 0 & 1 & $X$ & $X$ & $X$ \\`
292			`1 & 1 & 1 & 0 & $X$ & $X$ & $X$ \\`
293			`1 & 1 & 1 & 1 & $X$ & $X$ & $X$ \\`
294			`\hline`
295			`\end{tabular}`
296
297			`$q0$:`
298			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
299			`\hline`
300			`\multicolumn{6}{\|c\|}{$q_1 q_0$ } \\`
301			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
302			`& \tiny{$00$} & & & $X$ & \\`
303			`$e_0 e_1$ & \tiny{$01$} & & & $X$ & \\`
304			`& \tiny{$11$} & $X$ & $X$ & $X$ & $X$ \\`
305			`& \tiny{$10$} & & 1 & $X$ & \\`
306			`\hline`
307			`\end{tabular}`
308
309			$q_0^+ = q_0'. e_0$
310
311			`$q1$:`
312			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
313			`\hline`
314			`\multicolumn{6}{\|c\|}{$q_1 q_0$ } \\`
315			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
316			`& \tiny{$00$} & & & $X$ & \\`
317			`$e_0 e_1$ & \tiny{$01$} & 1 & & $X$ & 1 \\`
318			`& \tiny{$11$} & $X$ & $X$ & $X$ & $X$ \\`
319			`& \tiny{$10$} & 1 & & $X$ & \\`
320			`\hline`
321			`\end{tabular}`
322
323
324			$q_1^+ = q_1'. e_1$
325
326			`$S$:`
327			`\begin{tabular}{\|cc\|c\|c\|c\|c\|}`
328			`\hline`
329			`\multicolumn{6}{\|c\|}{$q_1 q_0 $ } \\`
330			`& & \tiny{$00$} & \tiny{$01$} & \tiny{$11$} & \tiny{$10$} \\`
331			`& \tiny{$00$} & & 1 & $X$ & 1 \\`
332			`$e_1 e_2$ & \tiny{$01$} & & & $X$ & 1 \\`
333			`& \tiny{$11$} & $X$ & $X$ & $X$ & $X$ \\`
334			`& \tiny{$10$} & & 1 & $X$ & \\`
335			`\hline`
336			`\end{tabular}`
337
338			$ S = q_0. e_0' + q_1. e_1' $
339
340
341			`\vspace{10pt}`
342
343			`\end{multicols}`
344
345			`%\hrule`
346
347
348			`\end{document}`
349