document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192134>Question 1192134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a k-map to simplify the following function:<BR>\n" );
document.write( "F(W, X, Y, Z) = X'Y' + XYZ' + WXY + W'X'Y' + WZ\r<BR>\n" );
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document.write( "Can I get an explanation of this homework question step-by-step please? 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 #849079 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=849079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to simplify the function F(W, X, Y, Z) = X'Y' + XYZ' + WXY + W'X'Y' + WZ using a K-map:\r<BR>\n" );
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document.write( "1. **Set up the K-map:**\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "          WZ<BR>\n" );
document.write( "      00  01  11  10<BR>\n" );
document.write( "WX 00  1   1   1   1  (X'Y')<BR>\n" );
document.write( "   01  0   0   1   0  (XYZ')<BR>\n" );
document.write( "   11  0   1   1   0  (WXY)<BR>\n" );
document.write( "   10  1   1   1   1  (W'X'Y' and WZ)<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "2. **Fill in the K-map:**\r<BR>\n" );
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document.write( "* X'Y' (W=0, X=0, Y=0): This covers the first row (00) entirely, regardless of Z.<BR>\n" );
document.write( "* XYZ' (X=1, Y=1, Z=0): This is the cell at WX=01, YZ=10.<BR>\n" );
document.write( "* WXY (W=1, X=1, Y=1): This is the cell at WX=11, YZ=11.<BR>\n" );
document.write( "* W'X'Y' (W=0, X=0, Y=0): This is already covered by X'Y'.<BR>\n" );
document.write( "* WZ: This term covers all cells where W=1 *or* Z=1.  The cells where W=1 are already covered by WXY and a portion of X'Y'. The cells where Z=1 are on the 01 and 11 columns.\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, 16).\r<BR>\n" );
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document.write( "* **Group 1:** The entire first row (X'Y') is a group of 4. This represents X'Y'.<BR>\n" );
document.write( "* **Group 2:** The 1s in the bottom row (W=1) are best grouped as a group of 4 (covering WZ). This represents W.<BR>\n" );
document.write( "* **Group 3:** The remaining '1' at WX=01 and YZ=10 is covered by XYZ'.\r<BR>\n" );
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document.write( "4. **Write the simplified expression:**\r<BR>\n" );
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document.write( "By combining the groups, we get the simplified Boolean expression:\r<BR>\n" );
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document.write( "F(W, X, Y, Z) = X'Y' + W + XYZ'\r<BR>\n" );
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document.write( "Therefore, the simplified function is **F(W, X, Y, Z) = X'Y' + W + XYZ'**.<BR>\n" );
document.write( " </SPAN>\n" );
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