Explicit expression of the interval algorithm for random number generation based on number systems

In this paper we analysis the interval algorithm for random number generation proposed by Han and Hoshi using the expression of real numbers on the interval [0,1). We first an explicit representation of the interval algorithm with the representation of real numbers on the interval [0,1) based one number systems. Next, using the expression of the interval algorithm, we give a rigorous analysis of the interval algorithm. We discuss the difference between the expected number of the coin tosses in the interval algorithm and their upper bound derived by Han and Hoshi and show that it can be characterized explicitly with the established expression of the interval algorithm.