A method and apparatus for generating random binary sequences from a physical entropy source having a state A and a state B by detecting whether the physical entropy source is in the state A or in the state B, attempting to shift the state of the physical entropy source to the opposite state in a probabilistic manner with less than 100% certainty, and producing one of four outputs based on the detected state and the state of the physical entropy source before the attempted shift. The outputs are placed in first and second queues and extracted in pairs from each queue. Random binary bits are output based on the sequences extracted from each queue.