Digital Arithmetic

Basic Fixed-Point Number Representation Systems 15

1.2,3

1.2,4

Sign Detection

We now present algorithms for sign detection in the sign-and-magnitude and

true-and-complement systems. Let

0 ifx >0

-- -

1.21

sign(x) 1 ifx <0

which allows representation of positive and negative 0s.

In the sign-and-magnitude system, the sign detection is trivial since there is

a sign bit.

In the true-and-complement system, since Ix l < C/2, the sign is determined

as follows: 3

0 ifxR

<C/2

sign(x)= 1 ifxR >C/2 1.22

Consequently, in the two's complement and ones' complement systems the sign

is determined from the most-significant bit as follows: ...