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,...
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