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or over 128,000 input vectors. Instead the designer selects a subset of tests. The three tests in <A HREF="CH13.c.htm#15122" CLASS="XRef">
Table 13.17</A>
check that all the bits of the output can be <SPAN CLASS="BodyComputer">
'0'</SPAN>
or <SPAN CLASS="BodyComputer">
'1'</SPAN>
. The two tests in <A HREF="CH13.c.htm#23812" CLASS="XRef">
Table 13.18</A>
make sure that the carry propagates through the adder, and that the adder can handle the largest numbers. The designer then repeats all of these five tests with the carry-in <SPAN CLASS="BodyComputer">
Cin</SPAN>
set to <SPAN CLASS="BodyComputer">
'1'</SPAN>
instead of <SPAN CLASS="BodyComputer">
'0'</SPAN>
. Next the designer performs a series of 24 tests using the three patterns shown in <A HREF="CH13.c.htm#13516" CLASS="XRef">
Table 13.19</A>
, with all eight possible combinations of <SPAN CLASS="BodyComputer">
'0'</SPAN>
and <SPAN CLASS="BodyComputer">
'1'</SPAN>
for <SPAN CLASS="BodyComputer">
x</SPAN>
, <SPAN CLASS="BodyComputer">
y</SPAN>
, and <SPAN CLASS="BodyComputer">
z</SPAN>
. These patterns test each full adder in isolation for all possible sum inputs (<SPAN CLASS="BodyComputer">
A</SPAN>
and <SPAN CLASS="BodyComputer">
B</SPAN>
) and carry input (<SPAN CLASS="BodyComputer">
Cin</SPAN>
). These tests appear comprehensive and reduce the number of vectors required from over 128,000 to 34. Confident, the designer releases the chip for fabrication. Unfortunately, the chip does not work. Which connections between adders did the designer’s tests fail to check?</P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="4">
<P CLASS="TableTitle">
<A NAME="pgfId=100559">
</A>
TABLE 13.17 <A NAME="15122">
</A>
Test to check for output toggling <BR>
(Problem <A HREF="CH13.c.htm#20482" CLASS="XRef">
13.29</A>
).</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100567">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="3">
<P CLASS="TableTitle">
<A NAME="pgfId=100571">
</A>
TABLE 13.18 <A NAME="23812">
</A>
Test to check for carry propagation (Problem <A HREF="CH13.c.htm#20482" CLASS="XRef">
13.29</A>
).</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100577">
</A>
<SPAN CLASS="BodyComputer">
A</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100579">
</A>
<SPAN CLASS="BodyComputer">
00000000</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100581">
</A>
<SPAN CLASS="BodyComputer">
00000000</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100583">
</A>
<SPAN CLASS="BodyComputer">
01010101</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100585">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100587">
</A>
<SPAN CLASS="BodyComputer">
A</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100589">
</A>
<SPAN CLASS="BodyComputer">
00000001</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100591">
</A>
<SPAN CLASS="BodyComputer">
11111111</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100593">
</A>
<SPAN CLASS="BodyComputer">
B</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100595">
</A>
<SPAN CLASS="BodyComputer">
00000000</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100597">
</A>
<SPAN CLASS="BodyComputer">
11111111</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100599">
</A>
<SPAN CLASS="BodyComputer">
10101010</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100601">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100603">
</A>
<SPAN CLASS="BodyComputer">
B</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100605">
</A>
<SPAN CLASS="BodyComputer">
11111111</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100607">
</A>
<SPAN CLASS="BodyComputer">
11111111</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100609">
</A>
<SPAN CLASS="BodyComputer">
Cin</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100611">
</A>
<SPAN CLASS="BodyComputer">
0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100613">
</A>
<SPAN CLASS="BodyComputer">
0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100615">
</A>
<SPAN CLASS="BodyComputer">
0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100617">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100619">
</A>
<SPAN CLASS="BodyComputer">
Cin</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100621">
</A>
<SPAN CLASS="BodyComputer">
0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100623">
</A>
<SPAN CLASS="BodyComputer">
0</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100625">
</A>
<SPAN CLASS="BodyComputer">
Sum</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100627">
</A>
<SPAN CLASS="BodyComputer">
000000000</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100629">
</A>
<SPAN CLASS="BodyComputer">
011111111</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100631">
</A>
<SPAN CLASS="BodyComputer">
011111111</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100633">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100635">
</A>
<SPAN CLASS="BodyComputer">
Sum</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100637">
</A>
<SPAN CLASS="BodyComputer">
100000000</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100639">
</A>
<SPAN CLASS="BodyComputer">
111111110</SPAN>
</P>
</TD>
</TR>
</TABLE>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="4">
<P CLASS="TableTitle">
<A NAME="pgfId=100650">
</A>
TABLE 13.19 <A NAME="13516">
</A>
Test with all possible combinations of <SPAN CLASS="BodyComputer">
'0'</SPAN>
and <SPAN CLASS="BodyComputer">
'1'</SPAN>
for <SPAN CLASS="BodyComputer">
x</SPAN>
, <SPAN CLASS="BodyComputer">
y</SPAN>
, and <SPAN CLASS="BodyComputer">
z</SPAN>
(Problem <A HREF="CH13.c.htm#20482" CLASS="XRef">
13.29</A>
).</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100658">
</A>
<SPAN CLASS="BodyComputer">
A</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100660">
</A>
<SPAN CLASS="BodyComputer">
xz0xz0xz</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100662">
</A>
<SPAN CLASS="BodyComputer">
z0xz0xz0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100664">
</A>
<SPAN CLASS="BodyComputer">
0xz0xz0x</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100666">
</A>
<SPAN CLASS="BodyComputer">
B</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100668">
</A>
<SPAN CLASS="BodyComputer">
yz0yz0yz</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100670">
</A>
<SPAN CLASS="BodyComputer">
z0yz0yz0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100672">
</A>
<SPAN CLASS="BodyComputer">
0yz0yz0y</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100674">
</A>
<SPAN CLASS="BodyComputer">
C</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100676">
</A>
<SPAN CLASS="BodyComputer">
0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100678">
</A>
<SPAN CLASS="BodyComputer">
z</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100680">
</A>
<SPAN CLASS="BodyComputer">
z</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=100682">
</A>
<SPAN CLASS="BodyComputer">
Sum</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100684">
</A>
<SPAN CLASS="BodyComputer">
cs0cs0cs0</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100686">
</A>
<SPAN CLASS="BodyComputer">
z0cs0cs0z</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=100688">
</A>
<SPAN CLASS="BodyComputer">
0cs0cs0cs</SPAN>
</P>
</TD>
</TR>
</TABLE>
<P CLASS="ExerciseHead">
<A NAME="pgfId=107268">
</A>
13.30 <A NAME="23701">
</A>
(*BSIM1 parameters, 120 min.) SPICE models are tangled webs. For example, there are two formats for the 69 UCB <A NAME="marker=107764">
</A>
BSIM1 transistor parameters: (1) using parameter names (<A HREF="CH13.a.htm#31851" CLASS="XRef">
Table 13.15</A>
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