Hexadecimal 2006-10-25 17:29:33 2006-10-26 10:35:56 Definition digital number system % 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 hexadecimal system} is a positional number system with base 16, using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.\, It offers a compact way of expressing binary numbers. In hexadecimal, all Mersenne numbers greater than 127 end with the digit F repeated several times, while all Fermat numbers greater than 17 are written with several significant zeroes book-ended by two 1's. The \PMlinkescapetext{term} hexadecimal is a mixed formation of a Greek begin and a Latin end.\, There is also a less used synonym {\em hexadecadic} of purely Greek \PMlinkescapetext{derivation}. Some divisibility tests in hexadecimal are: $n$ is divisible by 2 if its least significant digit is 0, 2, 4, 6, 8, A, C or E. $n$ is divisible by 4 if its least significant digit is 0, 4, 8 or C. $n$ is divisible by 8 if its least significant digit is 0, or 8. $n$ is divisible by 15 if it has digital root F. $n$ is of course divisible by 16 if it ends in a 0. $n$ is divisible by 17 if the difference of the odd placed digits and the even place digits of $n$ is a multiple of 17.