If I have 11, I'd like to perform some kind of bitwise operation and get 1010.

If I have 111, 101010.

If I have 101, 100010.

Can I do this? How?

If so, is it possible to do this arbitrarily, i.e., if I wanted to interleave 8 0-bits for 8 value-bits: 11101110 01101010 -> 11101110 00000000 01101010 00000000