A lot of research has been done on multiple-valued logic(MVL) such as ternary logic in these years. MVL reduces the number of necessary operations and also decreases the chip area that would be used. Carbon nanotube field effect transistors(CNTFETs) are considered a viable alternative for silicon transistors(MOSFETs). Combining carbon nanotube transistors and MVL can produce a unique design that is faster and more flexible. In this paper, we design a new half adder and a new multiplier by nanotechnology using a ternary logic, which decreases the power consumption and chip surface and raises the speed. The presented design is simulated using CNTFET of Stanford University and HSPICE software, and the results are compared with those of other studies. A lot of research has been done on multiple-valued logic (MVL) such as ternary logic in these years. MVL reduces the number of necessary operations and also decreases the chip area that would be used. Carbon nanotube field effect transistors (CNTFETs) are considered a viable alternative for silicon transistors (MOSFETs). Combining carbon nanotube transistors and MVL can produce a unique design that is faster and more flexible. In this paper, we design a new half adder and a new multiplier by nanotechnology using a ternary logic, which reduces the power consumption and chip surface and raises the speed. The presented design is simulated using CNTFET of Stanford University and HSPICE software, and the results are compared with those of other studies.