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In this paper, we propose a systematic design methodology in the category of hybrid-CMOS logic style. A huge library of circuits appropriate for low-power and high-speed applications can be obtained by employing the proposed design methodology. The methodology is before used for designing XOR/XNOR and demonstrates the excellence of the new design features. The question of whether the method can be taken advantage to design the function of Carry and its complement (Carry and InverseCarry), as the third important module of a full adder, and what to extend the answer contributes to move towards the general systematic design. All the presented designs as before have high driving capability, balanced full-swing outputs with less glitches and small number of transistors. Also these only consist of one pass-transistor in the critical path, which causes low propagation delay and high drivability. As known, hybrid-CMOS full adders can be divided into three modules, e.g., SUM, Carry and XOR. Optimising these modules has reduced power consumption, delay and the number of transistors of full adders. Therefore by embedding the balanced full-swing circuits in carry module, it can be expected that 11 new full adder circuits will possess high performance. Simulation results show that the proposed circuits exhibit better performances compared to previously suggested circuits in the proposed realistic test bench. These circuits, outperform their counterparts, are showing 24–126% improvement in the power-delay product (PDP) and 57–82% improvement in the area. All simulations have been performed with TSMC 0.13-μm technology in new full adder test bench, using HSPISE to achieve the minimum PDP. [ABSTRACT FROM AUTHOR]