# How do you add in base 8 the numbers 6_8, 54_8, 134_8 and 752_8 ?

Oct 18, 2017

${6}_{8} + {54}_{8} + {134}_{8} + {752}_{8} = {1170}_{8}$

#### Explanation:

Write the numbers in a list, right-aligned so we can add up the columns.

$\textcolor{w h i t e}{000} 6$
$\textcolor{w h i t e}{00} 54$
$\textcolor{w h i t e}{0} 134$
$\underline{\textcolor{w h i t e}{0} 752}$

In the units column, add $6$, $4$, $4$ and $2$ to get ${20}_{8}$ (i.e. ${16}_{10}$). So write a $0$ in the units column of the sum and carry $2$.

$\textcolor{w h i t e}{000} 6$
$\textcolor{w h i t e}{00} 54$
$\textcolor{w h i t e}{0} 134$
$\underline{\textcolor{w h i t e}{0} 752}$
$\textcolor{w h i t e}{000} 0$
$\textcolor{w h i t e}{00} \textcolor{g r e y}{2}$

In the eights column, add $5$, $3$, $5$ and our carry $2$ to get ${17}_{8}$ (i.e. ${15}_{10}$). So write a $7$ in the eights column of the sum and carry $1$.

$\textcolor{w h i t e}{000} 6$
$\textcolor{w h i t e}{00} 54$
$\textcolor{w h i t e}{0} 134$
$\underline{\textcolor{w h i t e}{0} 752}$
$\textcolor{w h i t e}{00} 70$
$\textcolor{w h i t e}{0} \textcolor{g r e y}{12}$

In the eight-squared column, add $1$, $7$ and our carry $1$ to get ${11}_{8}$ (i.e. ${9}_{10}$). So write a $1$ in the eight-squared column of the sum and carry $1$.

$\textcolor{w h i t e}{000} 6$
$\textcolor{w h i t e}{00} 54$
$\textcolor{w h i t e}{0} 134$
$\underline{\textcolor{w h i t e}{0} 752}$
$\textcolor{w h i t e}{0} 170$
$\textcolor{g r e y}{112}$

In the eight-cubed column, we just have our carry $1$, so write that in the eight-cubed column of the sum and stop.

$\textcolor{w h i t e}{000} 6$
$\textcolor{w h i t e}{00} 54$
$\textcolor{w h i t e}{0} 134$
$\underline{\textcolor{w h i t e}{0} 752}$
$1170$
$\textcolor{g r e y}{112}$