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In this paper, we present two new logic schemes to implement full adder cell using XOR-XNOR and NOR gates. Gate diffusion input (GDI) and modified GDI (MGDI) cells help to design low power circuits using less number of transistors. In this work, we design two new NOR gates based on MGDI cell. Then, using one of them and MGDI XOR-XNOR gates, two low-power and energy-efficient full adders which also meet full-swing property are proposed. The performance of our new full adders is evaluated and compared with some of the familiar full adders. Post-Layout simulations using Cadence Virtuoso tools in TSMC 0.18 μm CMOS process technology are carried out and the results show almost 24%–56% (22%–55%) and 36%–66% (28%–62%) improvements in the features power consumption and power-delay product (PDP), respectively. Also, full-swing property of our new adders are proved when they are subjected to all possible input combinations and transitions. [ABSTRACT FROM AUTHOR]