Quantum-dot cellular automata (QCA) nanotechnology has the capability to design highly-dense, ultra-low power, and high-speed digital circuits at ultra-deep sub-micron (ultra-DSM) level. QCA nanostructure provides a transistor-free operation that saves large energy dissipation as compared to the conventional metal oxide semiconductor field effect transistor (MOSFET) technology. In this paper, 3-input exclusive-OR (XOR) and exclusive-NOR (XNOR) gates are presented using QCA cells. XOR and XNOR (XOR-XNOR) gates are further utilized to design the 2-, 3-, 4-, and 5-bit even and odd parity generators. The QCA-based 3-input XNOR gate is constructed using only 10 QCA cells and two clock phases. The target of the presented designs is to use the minimum count of QCA cells in a simplistic way to form the higher bit-size parity generators. The comparative analyses for the different performance metrics are showing that the developed designs are performing well for the cell count, latency, area, and layout cost as compared to the existing designs. Energy dissipation for the designs is calculated to check the energy efficiency by using the QCA Designer-E and QCA Pro tools.