As with the conventional decimal expansion representation,
each real number is represented by an infinite decimal
sequence 
.
Digits may take on negative values as well as positive values:
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.
| Jeff Tupper | March 1996 |