For the first time, an area-efficient nonvolatile carry chain combining look-up tables and a pass-transistor-logic-based adder is newly developed using complementary atom switches without additional CMOS circuits. A proposed tristate switch composed of three pairs of complementary atom switches selects one of “0”, “1”, and the “carry_in” signal as the input of a common multiplexer for both a look-up table and an adder. The developed nonvolatile carry chain achieves the reductions of 20% area, 17% delay, and 17% power consumption, respectively, in comparison with a conventional nonvolatile carry chain using dedicated CMOS gates.