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2.15.6 Redundant Decimal Expansions

As with the conventional decimal expansion representation, each real number is represented by an infinite decimal sequence tex2html_wrap_inline33721 . Digits may take on negative values as well as positive values:

displaymath9007

This representation is used in hardware [9, 21, 31, 68], partially due to the on-line property mentioned above. The on-line property for real arithmetic using redundant decimal expansions can be specified as: the kth digit of the result is produced before the k+1+dth digits of the inputs are used. Circuits have been designed and built with small d. The on-line property implies that parallel addition circuits for this representation can operate without the regular carry propagation delay required by conventional decimal representations.


next up previous notation contents
Next: 2.15.7 Redundant Continued Fractions Up: 2.15 Real Representations Previous: 2.15.5 Converging Intervals
Jeff TupperMarch 1996