Digital Arithmetic

26 e x ApT E R I Review of Basic Number Representations and Arithmetic Algorithms

1.4

Range Extension and Arithmetic Shifts

We now present algorithms for range extension and arithmetic shifts for signed in-

tegers represented in the radix-2 system. The generalization to radix-r is straight-

forward. These operations are useful in the implementation of multiplication and

division.

1.4,'J

Range Extension

The range extension algorithm is performed when it is necessary to represent

the value x by a digit-vector of m digits, given its representation by a vector of n

digits (m > n). That is,

z =x 1.59

and

Z -- (Zm_l,

Zm_2,...