# CPS 209 Lecture Notes - Lecture 8: Positional Notation, Von Neumann Architecture, Mixed Radix

## Document Summary

Two fundamental principles: (1) an object is not the same things as its name or representation (2) there is nothing magical about number 10, except our universal convention of using it. We represent integers in: a base 10 positional number system so that each digit gives the magnitude of the power of 10 corresponding to that position. It is not enough just to see the individual digit, you must also see its position to know how much it is. Contrast this to roman numerals: where x is always ten. M is always one thousand no matter where it is positioned. A slight exception to this that if a smaller unit comes before a larger one, it is subtracted, not added. For example, xi is 11, but ix is 9. Every positive integer: has exactly one representation in this system, ignoring the leading zeros. By convention, the digits are written out right to left starting from least significant digit.