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logic networks of carry–save adders such as high-speed multipliers, multioperand adders, and double-rail input parallel adders are designed based on the parallel adders with a minimum number of NOR gates discussed in . After a discussion of the derivation of carry–save adder modules (CSAM's) by the integer programming logic design method, general design procedures are illustrated with example networks. Compared to conventional networks of carry–save adders, the derived networks of carry–save adder modules (NOCSAM's) have the advantages of fewer gates, fewer connections, and faster operation. In particular, the parallel adder of NOR gates in double-rail input logic obtained has six gates and 15½ connections per stage, whereas the previously known best design under the same condition requires six gates and 17 connections per stage with the same carry propagation delay.