Listing Patterns Systematically

There is a 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

To increase the number of bits (from one to two) make two copies of the list:

0
1

0
1

Within each copy, each row is unique. Now, make each row in the combined list unique. Do this by putting 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.