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Issue No. 11 - November (1998 vol. 47)
ISSN: 0018-9340
pp: 1244-1252
<p>Abstract—The prefix problem is to compute all the products <tmath>$x_1 \otimes x_2 \otimes \cdots \otimes x_k,$</tmath> for 1 ≤<it>k</it>≤<it>n</it>, where <tmath>$\otimes$</tmath> is an associative binary operation. We start with an asynchronous circuit to solve this problem with <it>O</it>(log <it>n</it>) latency and <it>O</it>(<it>n</it> log <it>n</it>) circuit size, with <tmath>$O(n)\ \otimes\!\!-{\rm operations}$</tmath> in the circuit. Our contributions are: 1) a modification to the circuit that improves its average-case latency from <it>O</it>(log <it>n</it>) to <it>O</it>(log log <it>n</it>) time, and 2) a further modification that allows the circuit to run at full-throughput, i.e., with constant response time. The construction can be used to obtain a asynchronous adder with <it>O</it>(log <it>n</it>) worst-case latency and <it>O</it>(log log <it>n</it>) average-case latency.</p>
Asynchronous circuits, binary addition, prefix computation, average-case latency.

R. Manohar and J. A. Tierno, "Asynchronous Parallel Prefix Computation," in IEEE Transactions on Computers, vol. 47, no. , pp. 1244-1252, 1998.
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