Digital Signal Processing Reference
In-Depth Information
FIGURE C.2.
Number wheel for signed integers.
resent the positive numbers and the left half the negative numbers, as shown in
Figure C.2. This representation is the 2's-complement system. The negative numbers
are the 2's complement of the positive numbers, and vice versa.
A 2's-complement binary integer,
Bb
=
◊◊◊
bb
n
-
1
1
0
is equivalent to the decimal integer
()
= -
n
-
1
1
0
IB
b
¥
2
+◊◊◊+
b
¥
2
+
b
¥
2
n
-
1
1
0
where the
b
's are binary digits. The sign bit has a negative weight; all the others have
positive weights. For example, consider the number
-
2,
3
2
1
0
1110
=- ¥
1
2
+ ¥
1
2
+ ¥
1
2
+
0
¥
2
=- +
8
4
+
2
+
0
=-
2
To apply the graphical technique to the operation 6
4, locate 6 on
the wheel, then step off (1110) units clockwise to arrive at the answer 4.
The binary addition of these same numbers,
+
(
-
2) mod16
=
0110
1110
10100
C
Search WWH ::
Custom Search