# Floating-Point Error in the NPR Media Player

The NPR Media Player apparently uses floating-point numbers to represent timestamps, based on this image (click it to enlarge):

NaNs in NPR Media Player (click image to enlarge).

# My Custom Binary Themed Calendar for 2010

I found twelve free stock images — all with binary themes — and made a custom calendar for 2010. Here’s May:

My Custom Binary-Themed Calendar For 2010

# How to Find the Last Digits of a Positive Power of Two

A common exercise in number theory is to find the last digits of a large power, like 22009, without using a computer. 22009 is a 605-digit number, so evaluating it by hand is out of the question. So how do you find its last digits — efficiently?

Modular arithmetic, and in particular, modular exponentiation, comes to the rescue. It provides an efficient way to find the last m digits of a power, by hand, with perhaps only a little help from a pocket calculator. All you need to do is compute the power incrementally, modulo 10m.

In this article, I will discuss three methods — all based on modular exponentiation and the laws of exponents — for finding the ending digits of a positive power of two. The techniques I use are easily adapted to powers of any number.