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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
Basic Multiplication Algorithms
29
x.q x..2 Xo
(" l j~ 1
(lost) 9 9149 0
/ /
Zn.l Zn-2 ZO
OVF
unless
Xn. 1 = Xn. 2
Xn.1 Xn.2
Zn.1 Zn-2
XO
/
Zo
OVF
unless
Xn. 1
=
Xn. 2
x,,q x,,.2 Xo
Zn-1 Zn-2 Zo
F ! G U R E 1.6
True-and-complement shift operations for r -- 2. (a) Two's complement left
shift. (b) Ones' complement left shift. (c) TC right shift.
The two's and ones' left arithmetic-shift algorithms are illustrated in Figure 1.6(a)
and (b). Proofs are left as Exercise 1.20.
In both the two's and ones' complement systems, the right arithmetic-shift
algorithm is
Zn_ 1 ~ Xn_ 1
Zi_ 1 -- Xi,
i =l,...,n-1
1.69
In this case, E
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Publisher Resources

ISBN: 9781558607989