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Digital Arithmetic
book

Digital Arithmetic

by Miloš D. Ercegovac, Tomás Lang
September 2003
Intermediate to advanced content levelIntermediate to advanced
709 pages
26h 51m
English
Morgan Kaufmann
Content preview from Digital Arithmetic
182
<: N,& {:, ~i ~ ~ g~ 4 Multiplication
o
This 2n-bit result is required because the range is
--(2n-1)(2 n-1 --
1) < p <
(--2n-1)(--2 n-l) -- 2 2n-2
4.4
so that the most positive value is represented by a vector of 2n bits.
IfxR, yR, and PR are the corresponding positive integer representa-
tions of x, y, and p, respectively, the high-level algorithm is
PR-
XRYR
22n -- (2 n --
XR)YR
22n --
XR( 2n -- YR)
(2 n
--XR)(2 n --YR)
ifx >0, y >0
if x < O, y > 0
if x > O, y < 0
if x < O, y < 0
4.5
As will be seen, this algorithm can be simplified when using the
corresponding digit-vectors.
In the next sections two types ...
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Publisher Resources

ISBN: 9781558607989