Hardware Reference
In-Depth Information
Example B.15
▼
Does overflow occur in the following 8-bit operations?
a. 01111111
2
2 00000111
2
b. 01100101
2
1 01100000
2
c. 10010001
2
2 01110000
2
Solution:
These subtraction operations are illustrated in Figure B.9 to B.11.
a. Negation of 00000111
2
is 11111001
2
. 01111111
2
2 00000111
2
is performed as follows:
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
+
1
Carry out to be discarded
Figure B.9
■
Example of addition that causes
no overflow
The difference is 01111000
2
5 120
10
. There is no overflow.
b. The sum of these two numbers is as follows:
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
+
The sign has changed from positive to negative
Figure B.10
■
Example of addition that
causes overflow
Overflow has occurred.
c
. The two's complement of 01110000
2
is 10010000
2
. 10010001
2
2 01110000
2
is performed as
follows:
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
+
Carry out to be discarded
1
.
The sign has changed from negative to positive
Figure B.11
■
Another example of addition that
causes overflow
Overflow has occurred.
▲
An important benefit of using two's complement arithmetic is that the same computer
hardware can perform signed and unsigned (all numbers are nonnegative) addition and subtrac-
tion without modification. It is up to the user to interpret the number to be negative.
Search WWH ::
Custom Search