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 Σrk2k, where rk equals a residue threshold function R(2k, 2k+1 |Z), defined by the proposition R(t, m |Z) ≡ t ⩽ (Σzi) mod m. The hardware realization is particularly simple using symmetry-adapted READ-ONLY storage (ROS) array logic.