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In this paper we designed a new type of Random number generator by using shift registers and LUT with D-FF as input to it. The algorithm used to generate random numbers is realized using simple xor circuit and implemented on a Virtex II FPGA from Xilinx. This designed block indicate a good sequence of random numbers which is used in high-speed data processor, Testing Instruments, Finding Laser Range, Timeof-flight mass spectrometry experiments etc. The randomness of this type of RNG is tested using NIST statistical test and this method has produced good results.