document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191388>Question 1191388</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, Z) = m0 + m2 + m5 + m7\r<BR>\n" );
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document.write( "Could you please explain to me this homework question step-by-step? Thank you! <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 #849101 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=849101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to simplify F(X, Y, Z) = m0 + m2 + m5 + m7 using a K-map:\r<BR>\n" );
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document.write( "1. **Set up the K-map:**  Since there are three variables (X, Y, and Z), the K-map will be a 2x4 grid:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "      YZ<BR>\n" );
document.write( "   00  01  11  10<BR>\n" );
document.write( "X 0  m0  m1  m3  m2<BR>\n" );
document.write( "  1  m4  m5  m7  m6<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "2. **Fill in the K-map based on the minterms:**\r<BR>\n" );
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document.write( "* m0: X=0, Y=0, Z=0  (top left cell)<BR>\n" );
document.write( "* m2: X=0, Y=1, Z=0  (top right cell)<BR>\n" );
document.write( "* m5: X=1, Y=0, Z=1  (bottom middle cell)<BR>\n" );
document.write( "* m7: X=1, Y=1, Z=1  (bottom right cell)\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "      YZ<BR>\n" );
document.write( "   00  01  11  10<BR>\n" );
document.write( "X 0  1   0   0   1<BR>\n" );
document.write( "  1  0   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, 8).\r<BR>\n" );
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document.write( "* **Group 1:** The two 1s in the top row can be grouped together. This represents X'Z' (X=0 and Z=0 for both cells).<BR>\n" );
document.write( "* **Group 2:** The two 1s in the bottom right corner can be grouped together. This represents XZ (X=1 and Z=1 for both cells).\r<BR>\n" );
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document.write( "4. **Write the simplified expression:**\r<BR>\n" );
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document.write( "F(X, Y, Z) = X'Z' + XZ\r<BR>\n" );
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document.write( "Therefore, the simplified function is **F(X, Y, Z) = X'Z' + XZ**.<BR>\n" );
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