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

  • Authors:
  • Irving T. Ho;Tien Chi Chen

  • Affiliations:
  • IBM Systems Products Division, Hopewell Junction, N.Y. 12533.;IBM Research Laboratory, San Jose, Calif. 95193.

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1973

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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 驴rk2k, where rk equals a residue threshold function R(2k, 2k+1 |Z), defined by the proposition R(t, m |Z) 驴 t 驴 (驴zi) mod m. The hardware realization is particularly simple using symmetry-adapted READ-ONLY storage (ROS) array logic.