The use of a redundant number system allows many arithmetic operations to process digits sequentially, mostsignificantdigitfirst. Final conversion back to a standard binary representation can require time to propag...
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The use of a redundant number system allows many arithmetic operations to process digits sequentially, mostsignificantdigitfirst. Final conversion back to a standard binary representation can require time to propagate any carries. This paper analyses and reports on the delays encountered when this is done by an online algorithm, giving a good upper bound on the expected delay. The delay is approximately log(i)k for the kth digit in a representation with base r.
An algorithm to convert redundant number representations into conventional representations is presented. The algorithm is performed concurrently with the digit-by-digit generation of redundant forms by schemes such as...
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An algorithm to convert redundant number representations into conventional representations is presented. The algorithm is performed concurrently with the digit-by-digit generation of redundant forms by schemes such as SRT division. It has a step delay roughly equivalent to the delay of a carry-save adder and simple implementation. The conversion scheme is applicable in arithmetic algorithms such as nonrestoring division, square root, and on-line operations in which redundantly represented results are generated in a digit-by-digit manner, from mostsignificant to least significant.
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