Answer
$10_{two}$
Work Step by Step
Start with the right-most column.
$1-1=0$
Record: $0_{two}$
$\begin{array}{lllll}
& 1 & 0 & 0 & 1_{two}\\
- & & 1 & 1 & 1_{two}\\
-- & -- & -- & -- &-- \\
& & & & 0_{two}
\end{array}$
Next column:
$0$ is less than $1$... borrow 1 $two$ from the $10_{two},$
because we can't borrow from zero.
$(0+2)-1=1$
Record the $1.$
$\begin{array}{lllll}
& 1 & 0 & 0 & 1_{two}\\
- & & 1 & 1 & 1_{two}\\
-- & -- & -- & -- &-- \\
& & & 1 & 0_{two}
\end{array}$
We are left with $10_{two}-1_{two}$,
but since we borrowed a two from the previous column,
the remaining subtraction is $1_{two}-1_{two}=0$,
which we do not record.
Result: $10_{two}$