<span>CMOS transistors are most widely used for the design of computerized circuits, when scaling down the nanometer technology these devices faces the short channel effects and causes I-V characteristics to depart from the traditional MOSFETs, So the researchers have developed the other transistors technologies like CNTFET and GNRFET. Carbon nanotube field effect transistor is one of the optimistic technologies and it is a three terminal transistor similar to MOSFET. The semiconducting channel between the two terminals called source and drain comprises of the nano tube which is made of carbon. Graphene nano ribbon filed effect transistor is the most optimistic technology here the semiconducting channel is made of graphene. When contrasted with barrel shaped CNTFETs, GNRFETs can be prepared in situ process, transfer-free and silicon compatible, thus have no passage related and alignment problems as faced in CNTFET devices. This paper presents different 1-bit Full Adder Cells (FACs) like TG MUX-based FAC (TGM), MN MUX-based FAC (MNM), proposed TG Modified MUX-based FAC (TGMM) and another proposed MN Modified MUX-based FAC (MNMM) are designed using different technologies like CNTFET and GNRFET at 16nm technology with supply voltage of 0.85v and simulation is done by using Synopsys HSPICE Tool and the proposed designs are best when compared to the TGM and MNM FACs in terms of Static and Dynamic powers Dissipations and Delay.</span>