Listing Patterns Systematically

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

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 unique each row in the combined list. Put "0" in front of each line of the first copy, and put "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.