The objective of this work is to implement a CNTFET-based ternary control unit and a ternary memory to be employed in a ternary processor. Ternary logic gives faster processing speed and Carbon Nanotube Field Effect Transistor (CNTFET) with its ballistic transport and nanometer size ensures low power and less area respectively. A ternary controller circuit is implemented with CNTFETs. C-Element, which is an integral part of the ternary controller circuit, is implemented with CNTFETs. It stores the previous output obtained by it until a new output is attained. This helps the controller to produce outputs according to stored values in the C-Element. The major component for power consumption in processors is the memory. This work also implements a ternary memory with CNTFETs. The simulation outputs with Cadence Virtuoso show superior performance in terms of speed and power when compared to the conventional methods. There is an improvement of at least 70% in the power delay product. By bringing ternary logic and CNTFET together, a low power and high speed processor can be implemented with the control unit and memory presented in this work. © 2017 IEEE.