http:^^www.cs.wisc.edu^~cs354-2^cs354^solutions^a3hw.ans.html

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Date: Tue, 05 Nov 1996 00:32:14 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Thu, 10 Oct 1996 20:02:36 GMTContent-length: 5639<!--This file created 9/27/96 4:08 PM by Claris Home Page version 1.0b1--><HTML><HEAD>   <TITLE>JT-HW3.ans.html</TITLE>   <X-SAS-WINDOW TOP=-49 BOTTOM=503 LEFT=-784 RIGHT=-111></HEAD><BODY><H1 ALIGN=CENTER><FONT SIZE=5>CS354, Fall 1996</FONT></H1><H1 ALIGN=CENTER><FONT SIZE=5>Homework 3, due Wednesday October 9 atthe start of class.</FONT></H1><H3><TABLE BORDER=1 CELLPADDING=1 WIDTH="100%" HEIGHT=35>   <TR>      <TD>         <P><B><FONT SIZE=4 COLOR="#AF0000">Name         (printed):</FONT></B>      </TD><TD>         <P><B><FONT SIZE=4 COLOR="#AF0000">Name (signed):</FONT></B>      </TD></TR></TABLE></H3><H3>Grader:</H3><P><TABLE BORDER=1 CELLPADDING=1 WIDTH="24%">   <TR>      <TD>         <P>Mohammad      </TD><TD>         <P>&nbsp;      </TD></TR>   <TR>      <TD>         <P>Sridevi      </TD><TD>         <P>&nbsp;      </TD></TR>   <TR>      <TD>         <P>Sunlung      </TD><TD>         <P>&nbsp;      </TD></TR></TABLE></P><H3>Total score:</H3><P><FONT COLOR="#000000">(1) (4 points) Find the largest IEEE 32 bitfloating point number that does not have an integer value. Expressthe answer in binary and in decimal.</FONT></P><BLOCKQUOTE><P><B><FONT COLOR="#000000">ANSWER</FONT></B></P><PRE><FONT COLOR="#000000">all FPS numbers larger than:100000000000000000000000.0</FONT><SUB><FONTCOLOR="#000000">2</FONT></SUB><FONT COLOR="#000000"> = 2</FONT><SUP><FONTCOLOR="#000000">23</FONT></SUP><FONT COLOR="#000000"> have integer valuessincethe significant only holds 23 bits&nbsp;the next smaller FPS number is: 11111111111111111111111.1</FONT><SUB><FONTCOLOR="#000000">2</FONT></SUB><FONT COLOR="#000000"> = 2</FONT><SUP><FONTCOLOR="#000000">23</FONT></SUP><FONT COLOR="#000000"> - 0.5 =8388607.5</FONT><SUB><FONT COLOR="#000000">10</FONT></SUB></PRE></BLOCKQUOTE><P><FONT COLOR="#000000">&nbsp;</FONT></P><P><FONT COLOR="#000000">(2) (2 points each, 6 points total) Writethe hexadecimal values for x, y and z just after the following codeexecutes:</FONT></P><BLOCKQUOTE><BLOCKQUOTE><BLOCKQUOTE><BLOCKQUOTE><BLOCKQUOTE><BLOCKQUOTE><BLOCKQUOTE><PRE><B><FONT COLOR="#000000">ANSWER</FONT></B></PRE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE><PRE><FONT COLOR="#000000">move x, 0x0f0fc123and  x, x, 0xff00f000      # x = 0x0f00c000not  x, x                  # x = 0xf0ff3fff &lt;- ansmove y, 0x8f0aabc9sll  y, y, 5               # y = 0xe1557920 &lt;- ansnor  z, x, y               # z = 0x0e008000 &lt;- ans</FONT></PRE></BLOCKQUOTE><P><FONT COLOR="#000000">&nbsp;</FONT></P><P><FONT COLOR="#000000">(3) (3 points each, 6 points total) Do thefollowing 2's complement multiplication. Indicate if eithercomputation overflows for 12 bit words, for 6 bit words. Show yourwork. Check your results by redoing the computation indecimal.</FONT></P><BLOCKQUOTE><PRE><FONT COLOR="#000000">          001010                                    001010</FONT><SUB><FONT COLOR="#000000">            </FONT></SUB><FONT COLOR="#000000">        x 111100                                  x 000011</FONT><SUB><FONT COLOR="#000000"></FONT></SUB><FONT COLOR="#000000">        --------                                  --------&nbsp;</FONT><B><FONT COLOR="#000000">ANSWER</FONT></B><FONT COLOR="#000000">&nbsp;    111111111100 &lt;-  sign extend the -4</FONT><SUB><FONTCOLOR="#000000">10</FONT></SUB><FONT COLOR="#000000">            001010 &lt;-  10</FONT><SUB><FONT COLOR="#000000">10</FONT></SUB><FONTCOLOR="#000000">          x 1010 &lt;-  10</FONT><SUB><FONTCOLOR="#000000">10</FONT></SUB><FONT COLOR="#000000">                          x 000011 &lt;-   3</FONT><SUB><FONT COLOR="#000000">10</FONT></SUB><FONTCOLOR="#000000">    ------------                                  --------   1111111111000                                    001010 111111111100                                      001010----------------                                  --------1001111111011000 &lt;- 011000 is 24</FONT><SUB><FONTCOLOR="#000000">10</FONT></SUB><FONT COLOR="#000000">                 0011110 &lt;-  011110 is 30</FONT><SUB><FONTCOLOR="#000000">10</FONT></SUB><FONT COLOR="#000000">                    in 6 bit, 2's comp                         in 6 bit, 2's comp</FONT><B><FONT COLOR="#000000">&nbsp;</FONT></B><FONT COLOR="#000000">111111011000</FONT><B><FONT COLOR="#000000"> </FONT></B><FONTCOLOR="#000000">is -40 in 12 bit 2's comp,            no overflow in 12 or 6 bitsno overflow for 12 bit words but overflowfor 6 bit words</FONT></PRE></BLOCKQUOTE><PRE><FONT COLOR="#000000">     </FONT></PRE><P><FONT COLOR="#000000">(4) (4 points) Show that the following twocode segments give the same value for c, for any values of a and b.Hint: consider truth tables (see page 116 of the text).</FONT></P><BLOCKQUOTE><PRE><FONT COLOR="#000000">and c, a, b          not c, anot c                not d, b                     or  c, c, d</FONT></PRE><P><B><FONT COLOR="#000000">ANSWER</FONT></B></P><PRE><FONT COLOR="#000000">the first sequence is not(a and b)while the second is (not(a) or not(b))column 4 and 7 of the following truth table are the sameso not(a and b) is the same as not(a) or not(b)&nbsp;a     b    (a and b)  not(a and b)   not(a)   not(b)   (not(a) or not(b))0     0        0           1           1        1              10     1        0           1           1        0              11     0        0           1           0        1              11     1        1           0           0        0              0</FONT></PRE></BLOCKQUOTE></BODY></HTML>

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