Abstract: A random number generator (RNG) using an analog-to-digital (A/D) converter to convert random noise into digital samples which are transformed by a reductive mapping into uniformly distributed random numbers for output. The synchronous RNG may be integrated and is intended for use in all computer systems. A noise source provides random noise from electronic events involving quantum-mechanical uncertainty. A compressor amplifies noise by a level-dependent gain to provide random noise, v (t), with a stabilized standard deviation and allows the output level of a noise source to vary without affecting the output of an RNG. An n-bit A/D converter converts v (t) into a digital random variable, Y. An expedient test of an RNG is to compute the mean and standard deviation of Y. Correlation is precluded by minimizing antialiasing. An interface circuit reduces Y modulo-M, where constant M<<2n, and generates random numbers, from 0 to M−1, at the A/D converter sampling frequency.