*Guest Author - Cathy Spearmon*

Example: Convert 25` 10` to octal

The division problem will be setup as 25` 10` ÷ 8

25

`÷ 8 = 3`

`10`

25

`– 24 = Remainder 1 -----> 1 (LSD)`

`10`

3 ÷ 8 = 0

3 – 0 = Remainder 3 -----> 3 (MSD)

Now, write the number from MSD to LSD as 31

`.`

`8`

This same process can be used regardless of the size of the decimal. Here is an example of a larger decimal.

Example: Convert 258` 10` to octal.

The division problem will be setup as 258` 10` ÷ 8

258

`÷ 8 = 32`

`10`

18 – 16 = Remainder 2 -----> 2 (LSD)

32 ÷ 8 = 4

32 – 32 = Remainder 0 -----> 0

4 ÷ 8 = 0

4 – 0 = Remainder 4 -----> 4 (MSD)

Now, write the number from MSD to LSD. You should end up with 402` 8`.

To convert a decimal fraction to octal, you must multiply the fraction by 8. Then, you need to extract the number(s) that appear to the left of the decimal point. The first number that is extracted will be the MSD and will follow the decimal point. The last number that is extracted will be the LSD. Continue to desired accuracy. This type of problem may result in results containing a mixed decimal number, which requires the whole number and the fraction to become split in order to achieve its equivalent octal conversion.

Example: Convert 0.175` 10` to octal.

The multiplication problem will be setup as

.0175`10`

__× 8__

0.1400 -----> 0 (MSD)

.1400

__× 8__

1.1200 -----> 1

.1200

__× 8__

0.9600 -----> 0

.9600

__× 8__

7.6800 -----> 7

.6800

__× 8__

5.4400 -----> 5

.4400

__× 8__

3.5200 -----> 3

.5200

__× 8__

4.1600 -----> 4

.1600

__× 8__

1.2800 -----> 1 (LSD)

Writing from MSD to LSD, you should end with .01075341` 8`.