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Given
X
and
Y
below that are 5bit numbers in 2’s complement form, ﬁll in the table of what
S
should be as a 5bit number in 2’s complement form (
even if the result causes an overﬂow
).
Indicate whether or not there is an
overﬂow
and what
S
is as a number (if
S
resu
ltsinanoverﬂow
,
then just put an “x” under the
S
column).
Also, in the last two columns, specify how the binary vector of
X
should be interpreted as an Octal
number and a Hexadecimal number, respectively?
(First two rows provide examples.)
X
Y
S
=
X
+
Y
S
in 2’s
X
in
X
in
x
4
x
3
x
2
x
1
x
0
y
4
y
3
y
2
y
1
y
0
s
4
s
3
s
2
s
1
s
0
Overﬂow?
complement
Octal
Hexadecimal
11101
10001
01110
yes
x
35
1D
00001
00111
01000
no
8
01
01
00111
01001
10000
yes
x
07
07
00111
10111
11110
no
2
07
07
11001
10111
10000
no
16
31
19
11001
01001
00010
no
2
31
19
Note:
X
= 11001 is the same for the last two rows. Hence
X
in Octal should be the same for the
last two rows as well. Same with
X
in Hexadecimal.
1
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(
A, B, C, D
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±
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 Spring '06
 Rosing

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