Question

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

Answer 1

`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.

`color(white)(000)6`
`color(white)(00)54`
`color(white)(0)134`
`underline(color(white)(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`.

`color(white)(000)6`
`color(white)(00)54`
`color(white)(0)134`
`underline(color(white)(0)752)`
`color(white)(000)0`
`color(white)(00)color(grey)(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`.

`color(white)(000)6`
`color(white)(00)54`
`color(white)(0)134`
`underline(color(white)(0)752)`
`color(white)(00)70`
`color(white)(0)color(grey)(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`.

`color(white)(000)6`
`color(white)(00)54`
`color(white)(0)134`
`underline(color(white)(0)752)`
`color(white)(0)170`
`color(grey)(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.

`color(white)(000)6`
`color(white)(00)54`
`color(white)(0)134`
`underline(color(white)(0)752)`
`1170`
`color(grey)(112)`