Source : Free On-Line Dictionary of Computing

two-to-the-N
     
        An amount much larger than {N} but smaller than {infinity}.
        "I have 2-to-the-N things to do before I can go out for lunch"
        means you probably won't show up.
     
        Numbers of the form two-to-the-N are very important in
        computing because they represent the value of bit N of a
        binary number (counting from 0) and the number of things you
        can count with an N bit number.
     
        [{Jargon File}]
     
        (1994-12-06)