Convert 34 from decimal to octal
(base 8) notation:
Power Test
Raise our base of 8 to a power
Start at 0 and increasing by 1 until it is >= 34
80 = 1
81 = 8
82 = 64 <--- Stop: This is greater than 34
Since 64 is greater than 34, we use 1 power less as our starting point which equals 1
Build octal notation
Work backwards from a power of 1
We start with a total sum of 0:
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 34 is 4
Multiplying this coefficient by our original value, we get: 4 * 8 = 32
Add our new value to our running total, we get:
0 + 32 = 32
This is <= 34, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 32
Our octal notation is now equal to 4
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 34 is 2
Multiplying this coefficient by our original value, we get: 2 * 1 = 2
Add our new value to our running total, we get:
32 + 2 = 34
This = 34, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 34
Our octal notation is now equal to 42
