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Total power dissipation in RSFQ circuits consists of two parts, dynamic and static. Dynamic power is dissipated in Josephson junctions performing useful logical and data transmission operations. This dissipation is fundamental and proportional to the data rate (at 4 K, of the order of 10/sup -18/ Joule per bit). Static power is dissipated in resistors used by RSFQ circuits to distribute dc bias current between Josephson junctions. This part of dissipation is not intrinsic to RSFQ circuits and in principle can be eliminated. The goal of this work is to show that Delay Insensitive (DI) RSFQ primitives can be modified so that resistors are no longer required in the dc power supply distribution network, so that the on-chip static power dissipation is absent. In this report we present the schematics for such primitives, define the class of circuits that allow resistor-free current distribution network, and formulate the requirements to the design of this network.