| 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? | ||||||||||||