APPENDIX A

Binary Numbers

This appendix could have been subtitled “How to do risk management on the back of a cocktail napkin.” Binary numbers are important in risk management for two reasons. First, most of the mathematics and statistics in this book will end up being implemented on computers. Implementation can often be as difficult as, if not more difficult than, the theoretical aspects of a problem. Even if you're not doing the programming yourself, understanding programming can make the transition from theory to working systems easier. Understanding programming means understanding computers, and binary is the language that computers speak. The second reason that binary numbers are of interest is that—just by chance—they provide a very useful shortcut for doing some very common calculations. Even if you're building highly complex systems, you'll often need to perform these back-of-the-envelope calculations.

Ordinarily, when we're doing arithmetic, we're using decimal numbers. If you see 157, this is usually shorthand for:

We say that decimal is base 10. Binary, by contrast, is base 2. In binary, 1,001 is shorthand for:

If you work this out, you'll see that binary 1,001 is equivalent to decimal 9.

Computers work in binary. The standard unit for most computers is the byte, which ...