I first saw this way to save the options on web form(many many "yes" and "no" options on admin form) was the VBB(vBulletin BBS in PHP https://www.vbulletin.com/), that's the way how they compress and save various options in just one int columen in mysql table.
10101010111 is same as many "yes" "no" checbox on web forms.

should be no 1

Huge thanks for those few who came up with this (double dabble) algorithm. Today I learned something new.
I think the best way to get your head around it is to look at it as a reverse of decimal to binary process.

Decimal to binary (https://www.cuemath.com/numbers/decimal-to-binary/):
To convert 13 to binary you need to:

1. 13 / 2 = 6 remainder 1
2. 6 / 2 = 3 remainder 0
3. 3 / 2 = 1 remainder 1
4. 1 / 2 = 0 remainder 1

So if we get remainders from bottom to top we end up with 1101, which is a binary representation of 13

If we use double dabble method, then we just put the above process in reverse.

• our number is 1 1 0 1 (so we start with leftmost digit - 1 and continue to the right)

1. 0 * 2 + 1 = 1 (does it remind you anything? Look at step 4 of decimal to binary process - 0 is quatinent and 1 is remainder)
2. 1 * 2 + 1 = 3 (look at the step 3 of decimal to binary)
3. 3 * 2 + 0 = 6
4. 6 * 2 + 1 = 13

One note: when using double dabble method we always start wit 0 * 2 (as there is no previous digit to the left-most digit of the binary number)

Hope this helps...

Makes perfect sense!
Thank you!