The signal processing in digital domain becoming ubiquitous, a full adder circuit module has gained prominence for its optimization in terms of its speed, power dissipation, noise margin and area. Further, with the advent of mobile applications on electronic devices, low power has emerged as an overriding design criterion. The proposed work aims to explore the design space of a low power full adder circuit and the implications of logic styles on power-delay trade-offs. Further, the issues impacting the selection of process for design for a given application are addressed. A 1-bit full adder circuit in static CMOS logic style and hybrid logic style is designed and optimized for low-power by carrying out exhaustive simulations using the LT spice simulator in 65 nm and 45 nm standard process to explore their power envelope, before low power process becomes necessary for design. Low power designs are demonstrated and the trade-offs with speed and area are explored.