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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
Adders with Redundant Digit Set
107
The two recodings are defined as follows:
Recoding 1
Xi
-~- Yi =
2hi+l +
Z i E
{-2, -1, 0, 1, 2} 2.105
such that hi E {0, 1} and
zi ~
{-2, - 1, 0}.
Consequently, the result of this recoding (addition) is
qi = 2;i -~- k i
2.106
with
qi E
{-2, -1, 0, 1}. Note that the computation ofqi does not have to be
done explicitly; that is, it can be kept as
zi
and
hi.
Recoding 2
qi
= 2ti+l -+-w
i E
{-2,-1, 0, 1}
2.107
such that
ti
~ {-1, 0} and
wi E
{0, 1}.
Consequently,
Si -- Wi -+- ti E
{-1, 0, 1} 2.108
Method 2: Using information from previous digit position. As before,
1.
Xi
+ Yi
= ...
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Publisher Resources

ISBN: 9781558607989