Page 481 - DSP Integrated Circuits

466 Chapter 11 Processing Elements

representation can be obtained from the corresponding positive number by adding
Q to the bit-complement. For example,

EXAMPLE 11.2

Show that the negative value of a number, x, in two's-complement representation
can be obtained by inverting all bits in the binary word and adding a 1 in the least
significant position.
We have

A useful property of two's-complement representation is that, if the sum lies
in the proper range, several two's-complement numbers can be added even though
the partial sums may temporarily overflow the available number range. Thus, the
numbers can be added in arbitrary order without considering possible overflow as
long as the final sum lies within the proper range.

EXAMPLE 11.3
Show by an example that the sum
of n (n > 3) numbers in two's-
complement representation can be
added without regard to overflows
of the partial sums if the final sum
is within the number range.
Assume that the numbers are

6/8 = (0.110) 2c, 4/8 = (0.100) 2C,
and -7/8 = (1.001) 2C.

We first add

Figure 11.1 Additions with overflow using
two's-complement numbers