Number system - arithmetic?

Question

Algorithms

There is an expression 2^300 + 2^200 - 101100

If we subtract 101.100 from 2^8 we get 110.100.00
If we subtract 101.100 from 2^10 we get 11.110.100.00
It turns out how many more zeros, so many more ones.

Then 2 ^ 200 - 101.100 will turn out (200-8 ones), 110.100.00

The final number will be
1.200 zeros, 192 ones, 110.100.00

As a result, 196 ones, and 205 zeros, the correct answer is 197 ones, and 204 zeros.

For a long time I can not find the error, help.

Answer 1

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111010100