Superconductive logic based on Josephson junctions (JJ) is a promising technology for energy efficient supercomputers and cloud computing. This technology can deliver significant improvements in performance and energy efficiency as compared to CMOS. Superconductive circuits, however, suffer from low density integration as compared to CMOS, primarily due to the limited scalability of the inductors. To improve the scalability of superconductive logic, a logic family based on a novel JJ technology, <inline-formula> <tex-math notation="LaTeX">$2\phi $ </tex-math></inline-formula>-JJ, has been proposed that eliminates the inductors. In this brief, three circuits are presented which exploit this scalable inductor-less technology. This novel <inline-formula> <tex-math notation="LaTeX">$2\phi $ </tex-math></inline-formula>-JJ technology represents the data as half flux quantum (HFQ) pulses, which improves the energy efficiency and speed as compared to standard superconductive logic such as rapid single flux quantum (RSFQ). Unlike RSFQ, the proposed circuits dynamically switch upon receiving an HFQ pulse, saving energy. These <inline-formula> <tex-math notation="LaTeX">$2\phi $ </tex-math></inline-formula>-JJ logic circuits operate 2.25X faster and require 2.6X less energy as compared to RSFQ.