Page 480 - DSP Integrated Circuits

11.2 Conventional Number Systems 465

EXAMPLE 11.1
Show that the negative value of a number, x, in one's-complement representation
can be obtained by inverting all bits in the binary word.
We have from Equation (11.10)

Hence, the sign of a number in one's-complement representation can be
changed by just taking the bit-complement. Thus, subtraction can be accomplished
by addition of the bit-complemented word.

A change of sign is easier in signed-magnitude representation compared to
binary offset and two's-complement representations, since using these representa-
tions, changing the sign of a number is done by taking the bit-complement and
adding 1 to the least-significant position. Multiplication using one's-complement is
more difficult to implement than with two's-complement or binary offset since an
end-around-carry is required.

11.2.4 Two's-Complement Representation
"Two's complement, three's a crowd"
Tony Platt, SAAB Military Aircraft

Two's-complement representation is a so-called radix complement representation
k
with R = r = 1 for r = 2 and k = 0. Two's-complement representation is the most
common type of arithmetic used in digital signal processing. The value of a nor-
malized W^-bit binary word in two's-complement representation is

-W d+l
The values lie in the range -1 < x < 1 - Q, where Q = 2 . There is one
more negative number than positive numbers and the value +1 can not be
represented. For x > 0 two's-complement has the same binary word as signed-
magnitude representation. The negative value of a number in two's-complement