document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191424>Question 1191424</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) = X’ + XY’\r<BR>\n" );
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document.write( "Can you explain this other homework question step-by-step please? Thanks again!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849096 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849096\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to simplify F(X, Y) = X' + XY' using a K-map:\r<BR>\n" );
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document.write( "1. **Set up the K-map:**  Since there are two variables (X and Y), the K-map will be a 2x2 grid:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "      Y<BR>\n" );
document.write( "   0   1<BR>\n" );
document.write( "X 0  X'Y' X'Y<BR>\n" );
document.write( "  1  XY'  XY<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "2. **Fill in the K-map based on the function:**\r<BR>\n" );
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document.write( "* **X'**: This term is true when X=0, regardless of the value of Y. So, we fill in both cells in the top row (X=0) with 1s.<BR>\n" );
document.write( "* **XY'**: This term is true when X=1 and Y=0.  So, we fill in the cell where X=1 and Y=0 with a 1.\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "      Y<BR>\n" );
document.write( "   0   1<BR>\n" );
document.write( "X 0  1   1<BR>\n" );
document.write( "  1  1   0<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "3. **Group the 1s:** We want to make the largest possible groups of 1s, where the groups are powers of 2 (1, 2, 4).\r<BR>\n" );
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document.write( "* **Group 1:** The two 1s in the top row form a group of 2. This group represents X' (because X=0 for both cells).<BR>\n" );
document.write( "* **Group 2:** The 1 at X=1 and Y=0 is already as large a group as it can be. This represents XY'.\r<BR>\n" );
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document.write( "4. **Write the simplified expression:**\r<BR>\n" );
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document.write( "The simplified expression is simply the sum of the groups:\r<BR>\n" );
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document.write( "F(X, Y) = X' + XY'\r<BR>\n" );
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document.write( "In this particular case, the function is *already simplified*. The K-map just confirms that there are no further simplifications possible.<BR>\n" );
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