Final answer:
There are 2^w distinct bit patterns that can reside in w bits, as every bit has 2 possible states and each can be independently set, leading to exponential growth in pattern count.
Step-by-step explanation:
When dealing with bits in computing, a bit pattern refers to any possible combination of zeros and ones that can fit into a given space of w bits. Since each bit in computing can either be a 0 or 1, for any bit position there are 2 possible values it can hold. When you have w bits, each one can be independently set to 0 or 1, leading to a total of 2w distinct bit patterns.
To visualize, if you have 1 bit, there are 21 = 2 possible patterns: 0 and 1. As you increase the number of bits to 2, the possibilities become 22 = 4, which are: 00, 01, 10, and 11. In general, for w bits the formula 2w is used.