Complementary metal oxide semiconductor (CMOS) is a low-power technology typically used in the efficient implementation of digital circuits. However, at nanodimensions, CMOS has problems due to its short channel effects and subthreshold leakage currents. These drawbacks can be overcome with quantum-dot cellular automata (QCA) which is one of the fastest nanotechnologies operated at THz rate. Thus, all digital circuits can now be implemented by QCA at the required nanoscale. This paper proposes a novel, energy-efficient and area-optimized 1-bit full adder design using QCA which provides efficient clocking, reduced cell count and reduced energy dissipation. The proposed design utilizes only 26 quantum cells in 0.02 µm2 area and has a reduction of 8% in number of cells, 75% in delay and 4% in energy dissipation at 1 K compared to the existing works. This innovative full adder design is used to implement a 4 × 4 Baugh–Wooley multiplier. The simulation results of the multiplier observed on QCADesigner 2.0.3 tool validate that the Baugh–Wooley multiplier designed with the novel 1-bit full adder yields better performance in terms of 9% reduction in area, 17.4% reduction in quantum cells used and reduced power dissipation of 2.44nW.