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Sheet1 Page 1 <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>CS231 Spring 2008 Homework 2 Solution</title> <link rel="stylesheet" type="text/css" href="/~cs231/style.css" /> <style type="text/css"> ol li { margin-top: 1em </style> </head> <body> <?xml version="1.0" encoding="us-ascii"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <h2 align="center">CS231 Spring 2008<br> Homework 2 Solution</h2> <hr /> <ol> <!-- ========== Problem 1 ========== --> <li>(15 pts) Use K-maps to simplify the following Boolean functions: <ol type="a"> <li><p>F( X, Y, Z ) = XY' + X'Y + X'Z + Y'Z' </li> <p><img src="1_a.png"></p> <p>F = X' + Y'</p> <li><p>F( A, B, C, D ) = ACD + A'BC + BD' + BC'D </li> <p><img src="1_b.png"></p> <p>F = B + ACD</p> <li><p>F( A, B, C, D ) = AB'C + A'B'C' + A'BC'D + B'CD' + C'D' </li> <p><img src="1_c.png"></p> <p>F = AB'C + A'C' + C'D' + B'D'</p> <p><img src="1_d.png"></p> <p>F = XY + XZ' + X'Y'Z</p> <p><img src="1_e.png"></p> <p>F = AB'C + A'B'C' + BD</p>
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Sheet1 Page 2 </ol> </li> <!-- ========== Problem 2 ========== --> <li>(15 pts) The following K-maps all attempt to show the function F with don't-care conditions d <blockquote> </blockquote> <p><img src="2.png"></p> <ol type="a"> <li><p>Which K-maps have invalid groupings? Explain.</p> <p>(i) is invalid because it has a 3x2 rectangle--all rectanglesmust be powers of 2.</p> <p>(iii) is invalid because it includes a 0 term (m3)</p> </li> <li><p>Of the remaining, valid K-maps, which have suboptimal groupings? Explain.</p> <p>(ii) is suboptimal because the green A'B'D' rectangle can be enlarged to become B'D'</p>
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