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| author | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
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| committer | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
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diff --git a/Bachelor/Digitaltechnik 2/SS07/P6/abel.ex1.html b/Bachelor/Digitaltechnik 2/SS07/P6/abel.ex1.html new file mode 100644 index 0000000..ec42f09 --- /dev/null +++ b/Bachelor/Digitaltechnik 2/SS07/P6/abel.ex1.html @@ -0,0 +1,176 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<html><head><title>Example of a Mealy Machine: string recognizer</title> + + + + <meta name="GENERATOR" content="User-Agent: Mozilla/3.0Gold (Macintosh; I; 68K)"> + <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 Mealy 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.." . When the machine is in the state S3 the output +will go high after the arrival of a "1" at the input. Thus the +output is associated with the <i>transitions</i> as indicated on the state +diagram.</p> + +<center><p><br> +<img src="abel.ex1-Dateien/abel_002.gif" height="101" width="262"><br> +<br> +</p></center> + +<p>Figure 1: State diagram, describing the sequence detector implemented +as a Mealy 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 with the "<font face="Courier">With</font>" +keyword to indicate that the output will change when the input goes to +one. <br> +</p> + +<p><font color="#000000">Listing 1: ABEL source code for the Mealy 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 Seqdet1</font></font> +</font></p> +</ul> + +<ul> +<p><font face="Courier"><font color="#000000"><font size="-1">Title 'Sequence +Detector 1011 with Mealy Machine'</font></font></font><br> +</p> + +<p><font face="Courier"><font color="#000000"><font size="-1">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">Q1, Q0 PIN istype 'reg';</font></font> +</font></p> + +<p><font size="-1"><font face="Courier"><font color="#000000">"State +register definitions</font></font> <br> +<font face="Courier"><font color="#000000">" and assignments of state +values</font></font> </font></p> + +<p><font size="-1"><font face="Courier"><font color="#000000">SREG = [Q1,Q0];</font></font> +<br> +<font face="Courier"><font color="#000000">S0 = [0,0];</font></font> <br clear="right"> +<font face="Courier"><font color="#000000">S1 = [0,1];</font></font> <br> +<font face="Courier"><font color="#000000">S2 = [1,0];</font></font> <br> +<font face="Courier"><font color="#000000">S3 = [1,1];</font></font></font><br> +</p> + +<p><font face="Courier"><font color="#000000"><font size="-1">Equations<br> +"Define the clock signal for the state machine</font></font></font></p> + +<p><font size="-1"><font face="Courier"><font color="#000000">[Q1,Q0].AR += RST;</font></font> <br> +<font face="Courier"><font color="#000000">[Q1,Q0].CLK =CLOCK;</font></font></font><br> +</p> + +<p><font size="-1"><font face="Courier"><font color="#000000">"Define +state diagram</font></font> </font></p> + +<p><font size="-1"><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: IF +X THEN S1 ELSE S0;</font></font> <br> +<font face="Courier"><font color="#000000">STATE S1: IF X THEN S1 ELSE +S2;</font></font> <br> +<font face="Courier"><font color="#000000">STATE S2: IF X THEN S3 ELSE +S0;</font></font> <br> +<font face="Courier"><font color="#000000">STATE S3: IF X THEN S1 WITH +Z=1; ELSE S2;</font></font></font><br> +</p> + +<p><font face="Courier"><font color="#000000"><font size="-1">end Seqdet1</font></font></font><br> +</p> +</ul> + +<p>The ouput is specified with the "With" keyword. The corresponding +simulation is shown in Figure 2. </p> + +<center><p><br> +<br> +<img src="abel.ex1-Dateien/abel_003.gif" height="333" width="548"><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>Notice that the output Z asserts as soon as the input is "1" +when in state S3. Comparing this output with the one obtained for a <a href="http://www.ese.upenn.edu/rca/software/abel/abel.ex2.html">Moore +machine</a> of the same sequence detector may let a casual observer think +that there is a timing problem as the output seems to asserts already after +the "101" input sequence. However, when one looks at the output +carefully one concludes that the waveform is correct. One has to realize +that the outputs are valid at the end of the state time (just before the +positive clock-edge) while the valid inputs are sampled just before the +positive clock edge as indicated in Figure 3 below. The input sequence +"1011" gives indeed an output sequence of "0001". </p> + +<center><p><img src="abel.ex1-Dateien/abel.gif" height="332" width="547"></p></center> + +<center><p>Figure 3: Output waveform of the Mealy machine (sequence detector +for "1011") with valid inputs and outputs indicated. (Screen +clip from Xilinx XACTstep(TM) Foundation software)</p></center> + +<p>One notices that there is a glitch in the output after the input sequence +10111010. However this occurs at a moment that the output is not valid +(the output is valid just before the positive clock edge). The valid output +sequence is than 000100000 as expected. </p> + +<p>This example indicates that one has to be very careful with the timing +when using a Mealy machine. Outputs can show glitches and are only valid +at the end of a state time (i.e. just before the the positive clock edge +for a positive edge triggered flip-flop or just before the negative clock +transition for a negative egde triggered flip-flop). On the other hand +a Mealy machine can often be implemented with fewer states that a Moore +machine as can be seen from the <a href="http://www.ese.upenn.edu/rca/software/abel/abel.ex2.html">Moore example</a>. +An alternative way to prevent glitches and to make the ouput of a Mealy +machine synchronous with the clock, it to use a synchronous Mealy machine. +The implementation of the sequence detector as a synchronous Mealy machine +is given in the <a href="http://www.ese.upenn.edu/rca/software/abel/abel.ex3.html">next example</a>.<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> +| To to <a href="http://www.ee.upenn.edu/rca/software/xilinx/foundation/commistakes.html">Common +Mistakes</a> list | Go to the <a href="http://www.ee.upenn.edu/rca">EE +Undergraduate Lab</a> Homepage | Go to <a href="http://www.ee.upenn.edu/rca/software/xilinx.html">Xilinx +Lab Tutorial</a> Homepage | Go to the <a href="http://www.ee.upenn.edu/rca/software/xilinx/foundation/foundation.sch1.html">Foundation +Tutorial</a> page | Go to <a href="http://www.seas.upenn.edu/%7Eee200/">EE200 +</a>or <a href="http://www.seas.upenn.edu/%7Eee200/lab/lab.html">EE200 Lab</a> +Homepage |</font><p></p> + +<p> +</p><hr width="100%">Created by J. Van der Spiegel: November 16, 1997; Updated +by J. Van der Spiegel: Dec. 30, 1997.<p></p> + + +</body></html>
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