Convert 47 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 >= 47
80 = 1
81 = 8
82 = 64 <--- Stop: This is greater than 47
Since 64 is greater than 47, 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 47 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 is <= 47, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 40
Our octal notation is now equal to 5
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 47 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
40 + 7 = 47
This = 47, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 47
Our octal notation is now equal to 57
