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In this paper we introduce a new flip-flop for use in a low- swing LC resonant clocking scheme. The proposed low-swing differential conditional capturing flip-flop (LS-DCCFF) operates with a low-swing sinusoidal clock through the utilization of reduced swing inverters at the clock port. The functionality of the proposed flip-flop was verified at extreme corners through simulations with parasitics extracted from layout. The LS-DCCFF enables 6.5% reduction in power compared to the full- swing flip-flop with 19% area overhead. In addition, a frequency dependent delay associated with driving pulsed flip-flops with a low-swing sinusoidal clock has been characterized. The LS-DCCFF has 870 ps longer data to output delay as compared to the full-swing flip-flop at the same setup time for a 100 MHz sinusoidal clock. The functionality of the proposed flip-flop was tested and verified by using the LS-DCCFF in a dual-mode multiply and accumulate (MAC) unit fabricated in TSMC 90-nm CMOS technology. Low-swing resonant clocking achieved around 5.8% reduction in total power with 5.7% area overhead for the MAC.