Answer
Consider a, 8- base number system, where there are digits 0-7in the number system. Also, take the numbers such that the sum of the numbers is bigger than the base.
\[\begin{align}
& \text{ 1 1} \\
& \text{ }162 \\
& +537 \\
& \text{ }\begin{matrix}
721 \\
\end{matrix} \\
\end{align}\]
For the above solution, first, add 7 and 2
\[\begin{align}
& {{2}_{eight}}+{{7}_{eight}}=9 \\
& ={{11}_{eight}}
\end{align}\]
Now add,
\[\begin{align}
& 6+3+1={{10}_{eight}} \\
& ={{12}_{eight}}
\end{align}\]
And,
\[5+1+1={{7}_{eight}}\]
The numbers are added in the same way as in the ten base. When the sum of 2 numbers become equal to or larger than the given base, use the mental conversions to convert the numeral from the 10-base to the required base (base-8 in this case).
