Answer
The difference in the indicated base is \[\text{1}{{1}_{\text{two}}}\].
Work Step by Step
Start by subtracting the numbers in the right-hand column:\[{{1}_{\text{two}}}-{{0}_{\text{two}}}\].
\[\begin{matrix}
\text{ 100}{{\text{1}}_{\text{two}}} \\
-\text{ }{{110}_{\text{two}}} \\
\text{ }1 \\
\end{matrix}\]
Now, subtract the numbers in the second column from the right: \[{{0}_{\text{two}}}-{{1}_{\text{two}}}\].
\[{{1}_{\text{two}}}\]is greater than \[{{0}_{\text{two}}}\].So, we need to borrow from the preceding column.
Now, borrow one group of 2 because in the provided question we are working in base two.
This gives a sum of \[2+0\] or 2 in base ten.
Now, subtract 1 from 2:
\[\begin{align}
& \text{ 12} \\
& \begin{matrix}
\text{ 100}{{\text{1}}_{\text{two}}} \\
-\text{ }{{110}_{\text{two}}} \\
\text{ 1}1 \\
\end{matrix} \\
\end{align}\]
Now, perform the subtraction in the third column from the right.
\[\begin{align}
& \text{ 12} \\
& \begin{matrix}
\text{ 100}{{\text{1}}_{\text{two}}} \\
-\text{ }{{110}_{\text{two}}} \\
\text{ 01}{{1}_{\text{two}}} \\
\end{matrix} \\
\end{align}\]
The difference in the indicated base is \[\text{1}{{1}_{\text{two}}}\].
