Below is a list of number sequences which follow a specific rule from one to the next. The first seven sequences are written out already. Can you deduce the next one?
1011111110111111011000
001111110011111001000
00111110001111000000
0111111001111100000
011111000111100000
01111000011100000
0111000001100000
???????????????
To assist in the solving process, I have made another sequence with a different beginning number.
1010010111101001001001
111011111111101101101
11001111111100100100
1000111111100000000
100111111110000000
10111111111000000
1111111111100000
???????????????
Hint:
Remember the base this puzzle uses, as well as another thing that involves parity.