MostSignificantDigit 2007-03-27 15:20:19 2007-03-27 15:20:19 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The {\em most significant digit} of a number $n$ written in a given positional base $b$ is the digit in the most significant place value, and has to be in the range $-1 < d_k < b$. In the case of an integer, the most significant digit is the $b^k$'s place value, where $k$ is the total number of digits, or $k = \lfloor log_{b} n \rfloor$. In an array of digits $k$ long meant for mathematical manipulation, it might be convenient to index the least significant digit with index 1 or 0, and the more significant digits with larger integers. (This enables the calculation of the value of a given digit as $d_ib^i$ rather than $d_ib^{k - i}$.) For an array of digits meant for text string manipulation, however, the most significant digit might be placed at position 0 or 1 (for example, by Mathematica's IntegerDigits function). In binary, the most significant digit is often called the {\em most significant bit}.