On the Distribution of the Most Significant Hexadecimal Digit

摘要

The report describes an investigation of the distribution of the most significant hexadecimal digit of numbers produced through scientific computing with the IBM-360 computer. Theoretical results are derived for the operations of multiplication, division, and addition (subtraction); these are compared, in some cases, with experimental results. It is shown that after certain sequences of operations, the distributions tend to be stable in the most significant hexadecimal digit and uniform in the number of leading zero binary bits in that digit. This leads to the uniform binary distribution, a very simple formula for obtaining the distribution of the leading hexadecimal digit d. Applications of the results of the study to truncation error analysis and function approximation are given. (Author)