Binary Number Memorization Systems
Memorizing binary data (e.g., 01110100010100100100...) is even easier than memorizing decimal numbers, because a larger number of digits can be encoded in a single locus. These techniques work on any type of binary data, including zeros and ones or the order of black and red in a deck of cards.
Contents 
Quick Binary Memorization Systems
These methods are very easy to learn, but probably aren't the most efficient for memory competitions. If you want to memorize binary numbers for memory competitions, see the section below on Complex Binary Memorization Systems.
The 8Letter Method
There are eight possible combinations of three binary digits:
 000 = None = N
 111 = All = A
 001 = Bottom = B
 100 = Top = T
 011 = Lower = L
 110 = Upper = U
 101 = Outer = O
 010 = Middle = M
110101 becomes U and O. Make a mnemonic image with the letters U and O, for example, "umbrella" and "opossum". Place those images in the first location in your Memory Palace, and then move on to the next six digits.
See this blog post for a full tutorial: Learn How to Memorize the Order of Black & Red in a Deck of Playing Cards (Easy)
Gary Lanier's Binary Method
This is an interesting system that was mentioned in Gary Lanier's memory journal in a post titled, Binary Numbers You Can See. In this system, mnemonic images are created from the shapes of the binary numbers:
 000 = the Three Stooges
 001 = glasses staring at a wall
 011 = bowling ball, 2pin split
 111 = three fence posts
 110 = a bull's two horns goring a matador's face
 100 = putter, golf ball, cup
 010 = a canon with a wheel on each side
 101 = a soccer ball making a goal
See also Number Shape System.
Complex Binary Memorization Systems
Number Conversion Systems
If you use a mnemonic system for decimal numbers like the Major System, Dominic System, or even Number Shape System or Number Rhyme System, you can convert the binary numbers to decimal like this:
 000 = 0
 001 = 1
 010 = 2
 011 = 3
 100 = 4
 101 = 5
 110 = 6
 111 = 7
It is highly recommended that you learn the correct way to count in binary. If you aren't familiar with it, check out this page.
Examples
If you have a onedigit system like the Number Shape System and your mnemonic image for 4 is a flag, then the binary number 100 would be represented by a flag.
If you have a twodigit system like the Major System or Dominic System, and the mnemonic image for 45 is a werewolf, then the binary number 100101 would be represented by a werewolf. If you are placing two images per locus in memory palaces, you can encode 12 binary digits per locus. If you are placing three images per locus, like in a PAO system, you can encode 18 binary digits per locus.
If you have a threedigit system, you could encode nine binary digits in a single image, and between 18 and 27 binary digits per locus.
Binary Grids
If binary numbers are combined into 3x3 grids of nine digits each, it only requires 512 images. The grids can be read from top to bottom, converting each row into a decimal digit.
For example, the following grid could use the same mnemonic image as 065, if you have a threedigit decimal number memorization system:
000 110 101
The reason for 065 is because:
 000 in binary is 0 in decimal
 110 in binary is 6 in decimal
 101 in binary is 5 in decimal
Practice grids can be found here and here. See also the binary training forum thread. There are also some image files of all 512 binary grids available.
Pros & Cons
The advantage to binary grids over something like the PAO system is that your images will exactly fit the 30 columns in a competition row. I.e., 30 digit rows divided by 3 digits width per image is 10 images per row. In contrast, a 2digit PAO system that encodes 18 binary digits per PAO set will have PAO sets that overlap the lines. The binary grid system will however only use 24 out of the 25 rows on a competition sheet (8x3). You can skip the last row, or use a different system on it.
The potential to miss 90 points for missing one image is one disadvantage to this system. This occurs because you take numbers from 3 rows for one image.
The differences in efficiency between this and the Ben System are that the grids only encode nine digits per image while the Ben System encodes 10. The grids require 512 images and the Ben System requires 1,024.
Ben System
The Ben System can encode 30 binary digits per locus, which is the exact number of digits in a row of binary numbers at memory competitions. The Ben System for binary numbers requires 1,024 mnemonic images and is significantly more complex that the simpler methods above. The technique is listed in the binary numbers section of the Ben System wiki page.
Comparison of Efficiency
For people who are interested in competition memorization, here is a table that compares the efficiency of different binary number memorization systems. The columns are the type of system, the rows are the number of images per location in a memory palace, and the table cells contain the number of binary digits that can be stored at each locus. For example, if you use a 2digit Major System and place three images per locus (e.g., PAO), you can encode 18 binary digits per locus.





 

1 image/locus  3  3  6  9  9  10 
2 images/locus  6  6  12  18  18  20 
3 images/locus  9  9  18  27  27  30 
The number of images required also varies greatly:
 a 9digit system (333) requires 512 images (8*8*8)
 a 10digit system (433) requires 1,024 images (16*8*8)
 an 11digit system (443) requires 2,048 images (16*16*8)
 a 12digit system (444) requires 4,096 images (16*16*16)