This research designs a discrete time (DT) chaos based random number generator (RNG), which uses one-dimension chaos modification as deterministic function in the destillation process. One-dimensional chaos (1D) is a simple dynamic system, which is widely applied to generate random numbers. Our work modifies logistic map that will be applied as DT chaos-based RNG. The logistic map is a chaotic system that is usually applied in the cryptosystem. The modification performed yields a new deterministic equations, which is capable to process data of real numbers, and generate positive and negative numbers. Through empirical verification the extractor function is obtained with the threshold value=0.718 to convert the real number that is generated by a deterministic function into a sequence of bits which has high entropy value. Through NIST 800-22 randomness test it is revealed that the obtained bit sequences have the proportion values at intervals 0.9804-0.9994 and P-values are greater than 0.01 for the frequency test, the cumulative sums test, the rank test, and a linear complexity test. Implementation of the DT chaos-based RNG method with the our proposed function using ZedBoard Zynq 7000 presents the number of resources used are LUT=3.9%, FF=1.6% and DSP =12.7%.