Bitstrings
N-bit number:
bN-1 bN-2...b1b0
Can also think of this as a string of digits 0 and 1.
How many possible patterns for N-bit string?
Each bit bi can have 2 possible values
There are N such bits
Therefore, total number of patterns is
2 * 2 * . . . * 2 = 2N (Important Binary Number Fact #1)
How many different VALUES? (trick question)
It depends on the representation being used.  (We will look at several.)
How many bits does it take to represent a given number N?