How did they do the math for panel 5 of this web comic? http://xkcd.com/936/

so 2^44 possibilities, 1000 guesses / second,

thus: 2^44 / 1000 seconds and then that can be converted to years:

2^44 / (1000 * 60 * 60 * 24 * 365) = 557.8 (years)

Imagine that you chose your password to be a number comprising 44 bits, each 1 or 0. How long would it take a computer to discover your password (with certainty) if it made 1000 guesses/second?

 

It needs to try all 2^44 possible numbers, and at the rate of 1000/sec this will take xxxx seconds, which you can convert to minutes, day, years, and it comes to 557.8 years before all possible 44-bit combinations of bits have been tried. Statistically, there is a good chance of hitting the password in half this time.