These charts were made fairly manually, and haven't yet been checked through an automated method. (For now, verify errors on your own or use at your own risk.)

Understanding Centermost counting

This documentation is based on left-to-right reading (like words found in standard English, and unlike words found in Hebrew or Arabic, but perhaps like numbers even in Hebrew and Arabic).

This is based on information from RFC 3531 section 3.3 or information derived from the logic of that RFC section.

Standard binary counting places the order of columns in MSB order (with the “most significant” bits on the left), so the values of each column are in this order:

128 64 32 16 8 4 2 1

RFC 1219 reverses it, placing the order of columns in LSB order (“least significant” bits on the left), so the values of each column are in this order:

1 2 4 8 32 16 32 64 128

RFC 3531's Centermost strategy orders columns in this order:

128 32 8 2 1 4 16 64

That is, it starts in the middle (offset a bit to the right if there is an even number of digits). The next column to be added is the column to the left of what is already used. The next column to be added is the column to the right of what is already used. (After that, once again, the next column to be added is the column to the left of what is already used. Then, the next column to be added is the column to the right of what is already used.) The pattern continues, flip-flopping between adding to the left and adding to the right.

So, after 0 (00000000 binary),
which is a subnet that should
probably be skipped
, the next
number is 8 (00001000 binary),
and then 16 (00010000 binary),
and then 24 (00011000 binary),
and then 4 (00000100 binary),
and then 12 (00001100 binary),
and then 20 (00010100 binary),
and then 28 (00011100 binary),

The following are 32 (00100000) higher than the numbers in the first chart.

32 (00100000 binary),
40 (00101000 binary),
48 (00110000 binary),
56 (00111000 binary),
36 (00100100 binary),
44 (00101100 binary),
52 (00110100 binary),
60 (00111100 binary)

2 (00000010 binary),
10 (00001010 binary),
18 (00010010 binary),
26 (00011010 binary),
6 (00000110 binary),
14 (00001110 binary),
22 (00010110 binary),
30 (00011110 binary)

(Some numbers below here are currently just provided in binary form.

34 (00100010 binary),
(00101010 binary),
(00110010 binary),
(00111010 binary),
(00100110 binary),
(00101110 binary),
(00110110 binary),
(00111110 binary)
So, after 64 (01000000 binary),
number is 72 (01001000 binary),
and then (01010000 binary),
and then (01011000 binary),
and then (01000100 binary),
and then (01001100 binary),
and then (01010100 binary),
and then (01011100 binary),
96 (01100000 binary),
(01101000 binary),
(01110000 binary),
(01111000 binary),
(01100100 binary),
(01101100 binary),
(01110100 binary),
(01111100 binary)
66 (01000010 binary),
(01001010 binary),
(01010010 binary),
(01011010 binary),
(01000110 binary),
(01001110 binary),
(01010110 binary),
(01011110 binary)
98 (01100010 binary),
(01101010 binary),
(01110010 binary),
(01111010 binary),
(01100110 binary),
(01101110 binary),
(01110110 binary),
(01111110 binary)

That is the first 8 charts.

The next 8 charts are like the first eight charts, but with one added (so they are all odd numbers).

The 8 charts after that are like the first eight charts, but with 128 added (so all the numbers will be even).

The 8 charts after that are like the first eight charts, but with 129 added (so, once again, they will all be odd numbers).