Convert 40 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 >= 40
80 = 1
81 = 8
82 = 64 <--- Stop: This is greater than 40
Since 64 is greater than 40, 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 40 is 5
Multiplying this coefficient by our original value, we get: 5 * 8 = 40
Add our new value to our running total, we get:
0 + 40 = 40
This = 40, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 40
Our octal notation is now equal to 5
The highest coefficient less than 7 we can multiply this by to stay under 40 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
40 + 1 = 41
This is > 40, so we assign a 0 for this digit.
Our total sum remains the same at 40
Our octal notation is now equal to 50