In this paper, novel circuits for XOR/XNOR and simultaneous XOR–XNOR functions are proposed. The proposed circuits are highly optimized in terms of the power consumption and delay, which are due to low output capacitance and low short-circuit power dissipation. We also propose six new hybrid 1-bit full-adder (FA) circuits based on the novel full-swing XOR–XNOR or XOR/XNOR gates. Each of the proposed circuits has its own merits in terms of speed, power consumption, power delay product (PDP), driving ability, and so on. To investigate the performance of the proposed designs, extensive HSPICE and Cadence Virtuoso simulations are performed. The simulation results, based on the 65-nm CMOS process technology model, indicate that the proposed designs have superior speed and power against other FA designs. A new transistor sizing method is presented to optimize the PDP of the circuits. In the proposed method, the numerical computation particle swarm optimization algorithm is used to achieve the desired value for optimum PDP with fewer iterations. The proposed circuits are investigated in terms of variations of the supply and threshold voltages, output capacitance, input noise immunity, and the size of transistors.