Currently, chaotic signal generators is of importance in cryptographic applications and chaotic communication systems. One of the significant field of the chaotic signal oscillators are random number generators. In this paper, an FPGA-based new true random number generator system using discrete-time chaotic signal generator is presented. The system designed incorporates the Sprott 94 G chaotic system based on an FPGA deployed with IEEE 754 standard. In order to produce random bits a quantification process has been performed on the results produced by the chaotic oscillator unit. Furthermore, the XOR method has been determined as restoring function to obtain a true random bit generator. The maximum operating frequency of FPGA-based true random number generator has been able to reach up to 399,383 MHz. The 20,000-bit sequence has been generated by the designed system and they have been saved to the test result file. They have been tested using NIST test suite and FIPS-140-1 standards and successful results have been obtained. It is concluded that the FPGA-based system is able to be used in cryptologic applications.