Two's Complement Wrap-Around
In this section, we give an example showing how temporary overflow in two's complement fixed-point causes no ill effects.
In 3-bit signed fixed-point arithmetic, the available numbers are as shown in Table 9.1.
|
Let's perform the sum , which gives a temporary overflow
(
, which wraps around to
), but a final result (
) which
is in the allowed range
:10.3

Now let's do in three-bit two's complement:

In both examples, the intermediate result overflows, but the final result is correct. Another way to state what happened is that a positive wrap-around in the first addition is canceled by a negative wrap-around in the second addition.
Next Section:
More about Potential Internal Overflow of DF-II
Previous Section:
Derivation of Group Delay as Modulation Delay