On the Distribution of Numbers

This paper examines the distribution of the mantissas of floating point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distributionr(x) = 1 x ln b (1/b x 1)(where b is the base of the number system). The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is included.