Convert decimal numbers into binary numbers

$1000_{(10)}=1023_{(10)}-23_{(10)}=1111111111_{(2)}-10111_{(2)}=1111101000_{(2)}$ In math, $a_{(2)}$ means it is a binary number, and $a_{(10)}$ means it is a decimal number. So $a_{(b)}$ means it is a base-b number.

Looking at the answer choices, it is clear that the answer must be $\boxed{1111101000}$ because it is the only one that has two terminating zeroes in its binary expansion. This is because $1000$ is divisible by $4$ .