Multiple Addition by Residue Threshold Functions and Their Representation by Array Logic

Abstract

In multioperand additions p summands can be compressed into q summands by adding along the columns independently. For a given column Z with Boolean elements {Zi}, this sum is ∑rk2k, where rk equals a residue threshold function R(2k, 2k+1|Z), defined by the proposition R(tm|Z) ≡ t ≤ (∑zi) mod m. The hardware realization is particularly simple using symmetry-adapted READ-ONLY storage (ROS) array logic. Copyright © 1973 by The Institute of Electrical and Electronics Engineers, Inc.