document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191396>Question 1191396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the following functions using a K-map\r<BR>\n" );
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document.write( "F(X, Y) = m2 + m3\r<BR>\n" );
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document.write( "Can you explain me this homework question step-by-step? Thank you very much!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823197 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Here are the standard minterms for 2 variables only.<BR>\n" );
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document.write( "<tr><TD colspan = 2></TD><TD  colspan = 2><center>Minterms</center></TD></tr><tr><TD >X</TD><TD >Y</TD><TD >Term</TD><TD >Designation</TD></tr><tr><TD >0</TD><TD >0</TD><TD >X'Y'</TD><TD >m0</TD></tr><tr><TD >0</TD><TD >1</TD><TD >X'Y</TD><TD >m1</TD></tr><tr><TD >1</TD><TD >0</TD><TD >XY'</TD><TD >m2</TD></tr><tr><TD >1</TD><TD >1</TD><TD >XY</TD><TD >m3</TD></tr>\n" );
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document.write( "This is the blank K-map for the two variables X and Y.<BR>\n" );
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document.write( "Along the top we have 0 and 1 corresponding to either X' or X respectively.<BR>\n" );
document.write( "Along the left side we have 0 and 1 corresponding to either Y' or Y respectively.<BR>\n" );
document.write( "These rules apply to minterms only.\r<BR>\n" );
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document.write( "Inside the table itself, we'll enter the m0 through m3 as shown below.<BR>\n" );
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document.write( "Here's some informal notation to help keep track.<BR>\n" );
document.write( "m0 = 00 = X'Y'<BR>\n" );
document.write( "m1 = 01 = X'Y<BR>\n" );
document.write( "m2 = 10 = XY'<BR>\n" );
document.write( "m3 = 11 = XY<BR>\n" );
document.write( "Or you could use the minterm table mentioned at the top of the page.\r<BR>\n" );
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document.write( "Next, we replace m2 and m3 with 1's since they are part of the F(X,Y) function.<BR>\n" );
document.write( "The other minterms get replaced with 0s<BR>\n" );
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document.write( "Now comes the grouping. <BR>\n" );
document.write( "Use these K-Map grouping rules<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karrules.html\">http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karrules.html</a><BR>\n" );
document.write( "and you can review on this page if needed<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karnaugh.html#introduction\">http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karnaugh.html#introduction</a><BR>\n" );
document.write( "There are a lot of rules to keep in mind, but once you get the hang of it, it's not too bad.\r<BR>\n" );
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document.write( "Luckily in this problem, we really don't have to bother with those rules because we have a fairly trivial grouping along the right column.<BR>\n" );
document.write( "So we end up with XY'+XY = X(Y'+Y) = X*1 = <font color=red>X</font>\r<BR>\n" );
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document.write( "Answer: <font color=red>X</font><BR>\n" );
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