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Asynchronous logic shows promising applicability in ASIC design due to its potentially low power and high robustness properties. For deep submicron technologies the static power is becoming very significant and many applications require that this power component to be reduced. A new logic called Positive Feedback Charge Sharing Logic (PFCSL) is proposed, which reduces both dynamic and especially static power and also could be implemented with asynchronous logic. This new logic combines adiabatic logic with charge sharing technology avoiding the penalty of power clock generator. A novel 16-by-16-bit Radix-4 Booth Multiplier is built based on PFCSL and implemented in 45nm technology. We achieve around 30% reduction in dynamic power and 60% in static power respectively compared to the same design being implemented using static dual-rail logic. Also, the area of the multiplier is significantly smaller.