Convert 20 from decimal to octal
(base 8) notation:
Raise our base of 8 to a power
Start at 0 and increasing by 1 until it is >= 20
80 = 1
81 = 8
82 = 64 <--- Stop: This is greater than 20
Since 64 is greater than 20, we use 1 power less as our starting point which equals 1
Work backwards from a power of 1
We start with a total sum of 0:
The highest coefficient less than 7 we can multiply this by to stay under 20 is 2
Multiplying this coefficient by our original value, we get: 2 * 8 = 16
Add our new value to our running total, we get:
0 + 16 = 16
This is <= 20, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 16
Our octal notation is now equal to 2
The highest coefficient less than 7 we can multiply this by to stay under 20 is 4
Multiplying this coefficient by our original value, we get: 4 * 1 = 4
Add our new value to our running total, we get:
16 + 4 = 20
This = 20, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 20
Our octal notation is now equal to 24