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This paper investigates the use of carbon nanotube field effect transistors (CNFETs) for the design of ternary full adder cells. The proposed circuits have been designed based on the unique properties of CNFETs such as having desired threshold voltages by adjusting diameter of the CNFETs gate nanotubes. The proposed circuits are examined using HSPICE simulator with the standard 32 nm CNFET technology. The proposed methods are simulated at different conditions such as different supply voltages, different temperature and operational frequencies. Simulation results show that the proposed designs are faster than the state of the art CNFET based ternary full adders.