Irving Tze Ho

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

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 {z_i}, this sum is Σr_k2^k, where r_k equals a residue threshold function R(2^k, 2^k+1 |Z), defined by the proposition R(t, m |Z) ≡ t ⩽ (Σz_i) mod m. The hardware realization is particularly simple using symmetry-adapted READ-ONLY storage (ROS) array logic.

Storage-efficient representation of decimal data

Usually n decimal digits are represented by 4n bits in computers. Actually, two BCD digits can be compressed optimally and reversibly into 7 bits, and three digits into 10 bits, by a very simple algorithm based on the fixed-length combination of two variable field-length encodings. In over half of the cases the compressed code results from the conventional BCD code by simple removal of redundant 0 bits. A long decimal message can be subdivided into three-digit blocks, and separately compressed; the result differs from the asymptotic minimum length by only 0.34 percent. The hardware requirement is small, and the mappings can be done manually.