A new approach for the design and hardware implementation of field programmable gate array (FPGA) general chaotic and hyperchaotic signal generators based on IEEE-754 standard is proposed. Firstly, using Euler algorithm and appropriate discrete processing, the continuous chaotic systems can be converted to discrete chaotic systems, which is appropriate for realization by digital signal processor. Secondly, according to IEEE-754 standard and module-based design idea, five basic floating-point operational modules, namely the multiplication operation module, addition operation module, symbolic function operation module, positive and negative absolute operation module, and initial and iteration value selection module, are constructed by using Verilog-HDL. Based on this method, different types of chaotic and hyperchaotic signals via FPGA are generated. Finally, using configurable voice device, chaotic signals are output through the stereo left and right channels and attractors can be observed by the oscillograph. The characteristic of this method is its universality. Furthermore, the floating-point algorithm and working principle are analyzed. The algorithm flow chart, technical development process, hardware design and realization result are given.