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 :
Now let's do in three-bit two's complement:
Thus, in both cases, 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.