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<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  What is an <FONT color="blue">computer program</FONT> ?
  </SPAN>
  </B></FONT>
  </div>


  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>

  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
<LI> <FONT color="red"><B>Computer program</B></FONT> =
     a <FONT color="blue"><B>series of instructions/commands</B></FONT> that is
     <FONT color="red"><B>executed</B></FONT> by the
   <FONT color="blue"><B>computer</B></FONT>
  <P>
    <FONT color="blue"><B>Note:</B></FONT> &nbsp;
<UL>
<TABLE bgcolor="lightyellow" BORDER="5" width=700>
<TR> <TD>
 <font size="+2">
 <UL>
 <LI> A <FONT color="red"><B>computer</B></FONT> is
     a <FONT color="blue"><B>machine</B></FONT> and
   <FONT color="red"><B>cannot think</B></FONT> !!!
 </UL>

</TD> </TR>
</TABLE>
</UL>
<P>
  <LI> <FONT color="red"><B>Some</B></FONT>
    <FONT color="blue"><B>computer programs</B></FONT> are
    used to <FONT color="red"><B>solve</B></FONT>
    <FONT color="blue"><B>complex problems</B></FONT>
<P>
<UL>
<TABLE bgcolor="lightyellow" BORDER="5" width=700>
<TR> <TD>
 <font size="+2">
 <UL>
 <LI> These 
    <FONT color="red"><B>computer programs</B></FONT> are
     called <FONT color="blue"><B>"algorithms"</B></FONT>
 </UL>

</TD> </TR>
</TABLE>
</UL>
<P>

    <LI> <FONT color="red"><B>Algorithm</B></FONT>
    = a <FONT color="blue"><B>step-by-step procedure</B></FONT>
      for <FONT color="red"><B>solving a problem</B></FONT>
    or <FONT color="blue"><B>accomplishing some task</B></FONT>
 <P>
 
 <P>
 <LI> A <FONT color="red"><B>computer algorithm</B></FONT> 
     <B>must</B> be <FONT color="blue"><B>spelled out</B></FONT>
     in <FONT color="red"><B>simple steps</B></FONT> that
     a <FONT color="blue"><B>(non-thinking) machine</B></FONT>
    (like a <FONT color="red"><B>computer</B></FONT>) can
   <FONT color="blue"><B>understand</B></FONT>
  
  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>

  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>







<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  What is <FONT color="blue">not</FONT> a
  computer algorithm
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>

  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
  <LI> <FONT color="red"><B>Consider</B></FONT> the
    following 
   <FONT color="blue"><B>steps</B></FONT> to
     <FONT color="red"><B>change a light bulb</B></FONT>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=650>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
  Remove the light bulb
  Insert a new light bulb </PRE></FONT></B></FONT>
  </TD> </TR>
  </TABLE>
  </center>

<P>
<LI> A <FONT color="red"><B>computer</B></FONT> cannot
   <FONT color="blue"><B>execute</B></FONT> these
   <FONT color="red"><B>steps</B></FONT> <B>because</B>:
<P>
<UL>
<TABLE bgcolor="lightyellow" BORDER="5">
<TR> <TD>
<font size="+2">
 <UL>
 <LI> A <FONT color="red"><B>computer</B></FONT> 
   <SPAN style="BACKGROUND-COLOR: #ffdd00">
    does 
     <FONT color="blue"><B>not understand</B></FONT></SPAN>
   
   <SPAN style="BACKGROUND-COLOR: #aaffaa">
   <FONT color="red"><B>how</B></FONT> to
   <FONT color="blue"><B>remove</B></FONT> a 
   <B>light bulb</B></SPAN>
 &nbsp;&nbsp;&nbsp;
 <P>
 <LI> A <FONT color="red"><B>computer</B></FONT> 
   <SPAN style="BACKGROUND-COLOR: #ffdd00">
    does 
     <FONT color="blue"><B>not understand</B></FONT></SPAN>
   
   <SPAN style="BACKGROUND-COLOR: #aaffaa">
   <FONT color="red"><B>how</B></FONT> to
   <FONT color="blue"><B>insert</B></FONT> a 
   <B>light bulb</B></SPAN>
 </UL>

</TD> </TR>
</TABLE>
</UL>
<P>
  <LI> <SPAN style="BACKGROUND-COLOR: #000000">
       <FONT color="yellow"><B>Remember</B></FONT></SPAN> that:
<P>
<UL>
<TABLE bgcolor="lightyellow" BORDER="5">
<TR> <TD>
<FONT SIZE="+2">

 <UL>
<LI> A <FONT color="red"><B>computer algorithm</B></FONT> 
     <B>must</B> be <FONT color="blue"><B>spelled out</B></FONT>
     in
     <SPAN style="BACKGROUND-COLOR: #aaffaa">
        <FONT color="red"><B>simple steps</B></FONT></SPAN> that
     a <FONT color="blue"><B>(non-thinking) machine</B></FONT>
    (like a <FONT color="red"><B>computer</B></FONT>) can
   <FONT color="blue"><B>understand</B></FONT>
   
 </UL>

</FONT>
</TD> </TR>
</TABLE>
</UL>
<P>
   
    
  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>


  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>




<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  What does a <FONT color="blue">computer algorithm</FONT>
  look like ?
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
 
  </font>
  </p>

  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
  <LI> A <FONT color="red"><B>computer algorithm</B></FONT> to
     <FONT color="blue"><B>change a light bulb</B></FONT>
    would look like <B>this</B>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=650>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
   <SPAN style="BACKGROUND-COLOR: #aaffaa">repeat until</SPAN> the <FONT color="red">light bulb comes out of socket</FONT>
   {
      <FONT color="red">turn</FONT> light bulb in <FONT color="red">counter-clockwise</FONT> direction
   }

   pick a new light bulb

   <SPAN style="BACKGROUND-COLOR: #aaffaa">repeat until</SPAN> the <FONT color="red">light bulb is secure in socket</FONT>
   {
      <FONT color="red">turn</FONT> light bulb in <FONT color="red">clockwise direction</FONT>
   }
</PRE></FONT></B></FONT>
  </TD> </TR>
  </TABLE>
  </center>

<P>
<LI> You can <B>see</B> that
   <FONT color="red"><B>computer algorithms</B></FONT> uses
   <FONT color="blue"><B>very simple operations</B></FONT>

  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>


  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>


<!---------- GCD ------------->




<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  A <FONT color="blue">famous algorithm</FONT> to find the
  <FONT color="blue">Greatest Common Divisor</FONT> of
  2 numbers
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>


  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
    <LI> <SPAN style="BACKGROUND-COLOR: #aaffaa">
	<FONT color="red"><B>Euclid's Algorithm</B></FONT></SPAN> to
       find the
  <FONT color="blue"><B>Greatest Common Divisor</B></FONT> of
   numbers
  <FONT color="red"><B><TT>A</TT></B></FONT> and
  <FONT color="red"><B><TT>B</TT></B></FONT>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=700>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
   Repeat until (<FONT color="red">A == 0 or B == 0</FONT>):        
   {
      if ( <FONT color="red">A > B</FONT> )
          replace <FONT color="red">A</FONT> with the value <FONT color="red">(A - B)</FONT>
      otherwise
          replace <FONT color="red">B</FONT> with the value <FONT color="red">(B - A)</FONT>
   }

   if ( <FONT color="red">A is not equal to 0</FONT> )
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">A</FONT>
   otherwise
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">B</FONT> </PRE></FONT></B></FONT>
  </TD> </TR>
  </TABLE>
  </center>
<P>
  <LI> <FONT color="red"><B>Recall</B></FONT> that
    a <SPAN style="BACKGROUND-COLOR: #aaffaa">
      <FONT color="blue"><B>computer</B></FONT></SPAN> can
    <FONT color="red"><B>perform</B></FONT>
    <SPAN style="BACKGROUND-COLOR: #ffff00">
       <FONT color="blue"><B>arithmetic operations</B></FONT></SPAN>, this
    <FONT color="red"><B>includes</B></FONT>
    <SPAN style="BACKGROUND-COLOR: #ffdd00">
      <FONT color="blue"><B>comparing</B></FONT>
    <FONT color="red"><B>2 numbers</B></FONT></SPAN> !

  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>


  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>





<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  A <FONT color="blue">famous algorithm</FONT> to find the
  <FONT color="blue">Greatest Common Divisor</FONT> of
  2 numbers
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>


  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
    <LI> <SPAN style="BACKGROUND-COLOR: #ffff00">
	<FONT color="red"><B>Sample execution</B></FONT></SPAN>
        of the <SPAN style="BACKGROUND-COLOR: #aaffaa">
	<FONT color="red"><B>Euclid's Algorithm</B></FONT></SPAN>:
<P>
<CENTER>
<TABLE bgcolor="lightyellow" BORDER="5" width=700>
<TR> <TD>

<FONT color="blue" size="+2">
<B>
<PRE>
   <FONT color="red">A</FONT> = 28      <FONT color="red">B</FONT> = 36 
</PRE>
</B>
</FONT>

</TD> </TR>
</TABLE>
</CENTER>
<P>
  <FONT color="red"><B>Steps</B></FONT>
  <FONT color="blue"><B>executed</B></FONT> by the
   <FONT color="red"><B>Euclid's Algorithm</B></FONT>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=700>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
   Repeat until <SPAN style="BACKGROUND-COLOR: #aaffaa">(<FONT color="red">A == 0 or B == 0</FONT>)</SPAN>:        
   {
      if ( <SPAN style="BACKGROUND-COLOR: #aaffaa"><FONT color="red">A > B</FONT></SPAN> )                        <SPAN style="BACKGROUND-COLOR: #aaffaa"> # 28 > 36 --> <FONT color="red">No</FONT>  </SPAN>
          replace <FONT color="red">A</FONT> with the value <FONT color="red">(A - B)</FONT>
      otherwise
          replace <FONT color="red">B</FONT> with the value <FONT color="red">(B - A)</FONT>   <SPAN style="BACKGROUND-COLOR: #ffdd00"> <--- do this </SPAN>
   }

   if ( <FONT color="red">A is not equal to 0</FONT> )
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">A</FONT>
   otherwise
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">B</FONT> </PRE></FONT></B></FONT>
  </TD> </TR>
  </TABLE>
  </center>

  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>


  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>


<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  A <FONT color="blue">famous algorithm</FONT> to find the
  <FONT color="blue">Greatest Common Divisor</FONT> of
  2 numbers
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>


  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
    <LI> <SPAN style="BACKGROUND-COLOR: #ffff00">
	<FONT color="red"><B>Sample execution</B></FONT></SPAN>
        of the <SPAN style="BACKGROUND-COLOR: #aaffaa">
	<FONT color="red"><B>Euclid's Algorithm</B></FONT></SPAN>:
<P>
<CENTER>
<TABLE bgcolor="lightyellow" BORDER="5" width=700>
<TR> <TD>

<FONT color="blue" size="+2">
<B>
<PRE>
   <FONT color="red">A</FONT> = 28      <FONT color="red">B</FONT> = <SPAN style="BACKGROUND-COLOR: #ffdd00">8</SPAN> 
</PRE>
</B>
</FONT>

</TD> </TR>
</TABLE>
</CENTER>
<P>
  <FONT color="red"><B>Steps</B></FONT>
  <FONT color="blue"><B>executed</B></FONT> by the
   <FONT color="red"><B>Euclid's Algorithm</B></FONT>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=700>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
   Repeat until <SPAN style="BACKGROUND-COLOR: #aaffaa">(<FONT color="red">A == 0 or B == 0</FONT>)</SPAN>:        
   {
      if ( <SPAN style="BACKGROUND-COLOR: #aaffaa"><FONT color="red">A > B</FONT></SPAN> )                        <SPAN style="BACKGROUND-COLOR: #aaffaa"> # 28 > 8 --> <FONT color="red">Yes</FONT>  </SPAN>
          replace <FONT color="red">A</FONT> with the value <FONT color="red">(A - B)</FONT>   <SPAN style="BACKGROUND-COLOR: #ffdd00"> <--- do this </SPAN>
      otherwise
          replace <FONT color="red">B</FONT> with the value <FONT color="red">(B - A)</FONT> 
   }

   if ( <FONT color="red">A is not equal to 0</FONT> )
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">A</FONT>
   otherwise
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">B</FONT> </PRE></FONT></B></FONT>
  </TD> </TR>
  </TABLE>
  </center>

  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>


  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>




<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  A <FONT color="blue">famous algorithm</FONT> to find the
  <FONT color="blue">Greatest Common Divisor</FONT> of
  2 numbers
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>


  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
    <LI> <SPAN style="BACKGROUND-COLOR: #ffff00">
	<FONT color="red"><B>Sample execution</B></FONT></SPAN>
        of the <SPAN style="BACKGROUND-COLOR: #aaffaa">
	<FONT color="red"><B>Euclid's Algorithm</B></FONT></SPAN>:
<P>
<CENTER>
<TABLE bgcolor="lightyellow" BORDER="5" width=700>
<TR> <TD>

<FONT color="blue" size="+2">
<B>
<PRE>
   <FONT color="red">A</FONT> = <SPAN style="BACKGROUND-COLOR: #ffdd00">20</SPAN>      <FONT color="red">B</FONT> = 8 
</PRE>
</B>
</FONT>

</TD> </TR>
</TABLE>
</CENTER>
<P>
  <FONT color="red"><B>Steps</B></FONT>
  <FONT color="blue"><B>executed</B></FONT> by the
   <FONT color="red"><B>Euclid's Algorithm</B></FONT>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=700>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
   Repeat until <SPAN style="BACKGROUND-COLOR: #aaffaa">(<FONT color="red">A == 0 or B == 0</FONT>)</SPAN>:        
   {
      if ( <SPAN style="BACKGROUND-COLOR: #aaffaa"><FONT color="red">A > B</FONT></SPAN> )                        <SPAN style="BACKGROUND-COLOR: #aaffaa"> # 20 > 8 --> <FONT color="red">Yes</FONT>  </SPAN>
          replace <FONT color="red">A</FONT> with the value <FONT color="red">(A - B)</FONT>   <SPAN style="BACKGROUND-COLOR: #ffdd00"> <--- do this </SPAN>
      otherwise
          replace <FONT color="red">B</FONT> with the value <FONT color="red">(B - A)</FONT> 
   }

   if ( <FONT color="red">A is not equal to 0</FONT> )
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">A</FONT>
   otherwise
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">B</FONT> </PRE></FONT></B></FONT>
  </TD> </TR>
  </TABLE>
  </center>

  </UL>
  </font>
  </TD> </TR>
  </TABLE>
  </center>


  <p style="margin-left: 1.2in">
  <font size="+2">
  </font>
  </p>

  <p style="padding: 0.0in">
  </p>
</div>


<div class="mySlides">
  <div class="text">
  <FONT color="red" size=+2><B>
  <SPAN style="BACKGROUND-COLOR: yellow">
  A <FONT color="blue">famous algorithm</FONT> to find the
  <FONT color="blue">Greatest Common Divisor</FONT> of
  2 numbers
  </SPAN>
  </B></FONT>
  </div>

  <p style="margin-left: 1.2in">
  <font size="+2">
  
  </font>
  </p>


  <center>
  <TABLE bgcolor="lightcyan" BORDER="5" width=850>
  <TR> <TD>
  <font size="+2">
  <UL>
    <LI> <SPAN style="BACKGROUND-COLOR: #ffff00">
	<FONT color="red"><B>Sample execution</B></FONT></SPAN>
        of the <SPAN style="BACKGROUND-COLOR: #aaffaa">
	<FONT color="red"><B>Euclid's Algorithm</B></FONT></SPAN>:
<P>
<CENTER>
<TABLE bgcolor="lightyellow" BORDER="5" width=700>
<TR> <TD>

<FONT color="blue" size="+2">
<B>
<PRE>
   <FONT color="red">A</FONT> = <SPAN style="BACKGROUND-COLOR: #ffdd00">12</SPAN>      <FONT color="red">B</FONT> = 8 
</PRE>
</B>
</FONT>

</TD> </TR>
</TABLE>
</CENTER>
<P>
  <FONT color="red"><B>Steps</B></FONT>
  <FONT color="blue"><B>executed</B></FONT> by the
   <FONT color="red"><B>Euclid's Algorithm</B></FONT>:
<P>
  <center>
  <TABLE bgcolor="lightyellow" BORDER="5" width=700>
  <TR> <TD>
  <FONT color="blue"><B><font size="+2"><PRE>
   Repeat until <SPAN style="BACKGROUND-COLOR: #aaffaa">(<FONT color="red">A == 0 or B == 0</FONT>)</SPAN>:        
   {
      if ( <SPAN style="BACKGROUND-COLOR: #aaffaa"><FONT color="red">A > B</FONT></SPAN> )                        <SPAN style="BACKGROUND-COLOR: #aaffaa"> # 12 > 8 --> <FONT color="red">Yes</FONT>  </SPAN>
          replace <FONT color="red">A</FONT> with the value <FONT color="red">(A - B)</FONT>   <SPAN style="BACKGROUND-COLOR: #ffdd00"> <--- do this </SPAN>
      otherwise
          replace <FONT color="red">B</FONT> with the value <FONT color="red">(B - A)</FONT> 
   }

   if ( <FONT color="red">A is not equal to 0</FONT> )
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">A</FONT>
   otherwise
      The <FONT color="red">Greatest Common Divisor</FONT> = <FONT color="red">B</FONT> </PRE></FONT></B></FONT>
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