Modern integrated circuits based on CMOS gates. COMS gates have high scalability ratios according to Moore's law but with the problem of high energy consumption. One emerging solution is to use Quantum-dot Cellular Automata (QCA) nanotechnology. The data transfer and computation rely on the interaction between nearby QCA cells. Some interesting features of QCA nanotechnology, such as high speed, small size, high scalability ratios and low energy consumption, make it an alternative solution to CMOS-based logic circuits. This paper proposes a 2-bit equality comparator using two new modified QCA-based EX-NOR gates. The first proposed design structure is called the base design, while the second one is called the improved design. QCADesigner version 2.0.3 tool and QCADesigner-E tool were used to evaluate the functionality and energy consumption of the two design structures, respectively. A comparison between the two design structures shows that the improved design requires a smaller number of cells, less occupied area, less cost and less energy consumption than that for the base design, while the result shows an equal amount of delay consumed by the two designs.