Is the number of patterns that can be formed with N bits greater than the number of bits?
Yes ― much greater. This simple fact is of profound importance to computer science.
Here is the standard method for listing all of the patterns that can be formed with a given number of bits.
First, list all of the patterns that can be formed with one bit:
0 1
Make two copies of the list:
0 1 0 1
Make each row unique. Put a "0" in front of each line of the first copy, and a "1" in front of each line of the second copy:
0 0 0 1 1 0 1 1
Now each line is unique and you have a complete list of the possible patterns of two bits. The number of unique patterns with 2 bits is double that with 1 bit.
For additional bits, repeat the trick for each new bit.
Each additional bit doubles the number of patterns.
How many patterns can be formed from three bits?