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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<html><head><title>Finite State Machine (Moore) example: string detector</title>
<meta name="GENERATOR" content="User-Agent: Mozilla/3.0Gold (Macintosh; I; PPC)">
<meta name="Author" content="J. Van der Spiegel"></head><body>
<h1 align="center"><i><font size="+1">University of Pennsylvania</font></i>
</h1>
<center><p><i><font size="+1">Department of Electrical Engineering </font></i><br>
<br>
</p></center>
<center><p><b>Finite State Machine implemented as a Moore Machine: </b></p></center>
<center><p><b>a non-resetting sequence recognizer.</b><br>
</p></center>
<p>The following state diagram (Fig. 1) describes a finite state machine
with one input X and one output Z. The FSM asserts its output Z when it
recognizes the following input bit sequence: "1011". The machine
will keep checking for the proper bit sequence and does not reset to the
initial state after it has recognized the string. As an example the input
string X= "..1011011..." will cause the output to go high twice:
Z = "..0001001.." . The output will asserts only when it is in
state S4 (after having seen the sequence 1011). The FSM is thus a Moore
machine.<br>
<br>
</p>
<center><p><img src="abel.ex2-Dateien/abel_002.gif" height="94" width="336"></p></center>
<p>Figure 1: State diagram, describing the sequence detector implemented
as a Moore machine. The number in italics underneath the states indicate
which part of the sequence the state remembers.<br>
</p>
<p>This state diagram can be described in ABEL code given in Listing 1.
The output is described after the STATE Si: statement. <br>
</p>
<p><font color="#000000">Listing 1: ABEL source code for the Moore machine
implementation of the sequence detector described in Fig. 1</font><br>
</p>
<ul>
<p><font size="-1"><font face="Courier"><font color="#000000">module Seqdet2</font></font>
<br>
<font face="Courier"><font color="#000000">Title 'Sequence detector implemented
as Moore machine'<br>
Declarations<br>
"input and output signals</font></font></font></p>
<p><font size="-1"><font face="Courier"><font color="#000000">X, CLOCK, RST
PIN;</font></font> <br>
<font face="Courier"><font color="#000000">Z PIN istype 'com';</font></font>
<br>
<font face="Courier"><font color="#000000">Q2, Q1, Q0 PIN istype 'reg';</font></font>
</font></p>
<p><font size="-1"><font face="Courier"><font color="#000000">"State
register declarations</font></font> </font></p>
<p><font size="-1"><font face="Courier"><font color="#000000">SREG = [Q2,Q1,Q0];</font></font>
<br>
<font face="Courier"><font color="#000000">S0 = [0,0,0];</font></font>
<br>
<font face="Courier"><font color="#000000">S1 = [0,0,1];</font></font>
<br>
<font face="Courier"><font color="#000000">S2 = [0,1,0];</font></font>
<br>
<font face="Courier"><font color="#000000">S3 = [0,1,1];</font></font>
<br>
<font face="Courier"><font color="#000000">S4 = [1,0,0];</font></font></font><br>
</p>
<p><font face="Courier"><font color="#000000"><font size="-1">Equations<br>
"Definition of the state machine clock signal</font></font></font></p>
<p><font size="-1"><font face="Courier"><font color="#000000">[Q2,Q1,Q0].AR
= RST;</font></font> <br>
<font face="Courier"><font color="#000000">[Q2,Q1,Q0].CLK = CLOCK;</font></font></font><br>
</p>
<p><font size="-1"><font face="Courier"><font color="#000000">"Define
state diagram</font></font> <br>
<font face="Courier"><font color="#000000">STATE_DIAGRAM SREG</font></font>
</font></p>
<p><font size="-1"><font face="Courier"><font color="#000000">STATE S0: Z=0;</font></font>
</font></p>
<ul>
<p><br>
<font size="-1"><font face="Courier"><font color="#000000">IF X THEN S1 ELSE
S0;</font></font> </font></p>
</ul>
<p><font size="-1"><font face="Courier"><font color="#000000">STATE S1: Z=0;</font></font>
</font></p>
<ul>
<p><font size="-1"><font face="Courier"><font color="#000000">IF X THEN S1
ELSE S2;</font></font> </font></p>
</ul>
<p><font face="Courier"><font color="#000000"><font size="-1">STATE S2: Z=0;
</font></font></font></p>
<ul>
<p><font size="-1"><font face="Courier"><font color="#000000">IF X THEN S3
ELSE S0;</font></font> </font></p>
</ul>
<p><font size="-1"><font face="Courier"><font color="#000000">STATE S3: Z=0;</font></font>
</font></p>
<ul>
<p><font size="-1"><font face="Courier"><font color="#000000">IF X THEN S4
ELSE S2;</font></font> </font></p>
</ul>
<p><font size="-1"><font face="Courier"><font color="#000000">STATE S4: Z=1;</font></font>
</font></p>
<ul>
<p><font size="-1"><font face="Courier"><font color="#000000">IF X THEN S1
ELSE S2;</font></font> </font></p>
</ul>
<p><font face="Courier"><font color="#000000"><font size="-1">end Seqdet2</font></font></font><br>
</p>
</ul>
<p>The corresponding simulation is shown in Figure 2. </p>
<center><p><br>
<img src="abel.ex2-Dateien/abel.gif" height="334" width="537"><br>
<br>
</p></center>
<center><p>Figure 2: Simulation of the sequence detector (for "1011")
described with the state diagram of Fig. 1. (Screen clip from Xilinx XACTstep(TM)
Foundation software)<br>
</p></center>
<p>One notices that the output asserts after the input sequence 1011 as
specified.<br>
</p>
<p>
</p><hr width="100%"><font size="-1">Back to ABEL Primer <a href="http://www.ee.upenn.edu/rca/software/abel/abel.primer.html#Contents">Contents</a>
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<p>
</p><hr width="100%">Created by J. Van der Spiegel: November 16, 1997. Updated
by J. Van der Spiegel, Nov. 19, 1997.<br>
<p></p>
</body></html>
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