The fix for the noncontiguous addition puzzle is to change

  filled = to & mask

to

  filled = to | ^mask

In other words, to OR in 1-bits so the carry can travel across the irrelevant part of the register.

Subtraction is similar:

https://bugfix-66.com/adbc40fa7c8c838d8d34bcd35525313dc91dea...

But for subtraction you want to AND in 0-bits so the borrow can travel.