Convert 107 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 >= 107
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 107
Since 512 is greater than 107, we use 1 power less as our starting point which equals 2
Build octal notation
Work backwards from a power of 2
We start with a total sum of 0:
82 = 64
The highest coefficient less than 7 we can multiply this by to stay under 107 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 107, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our octal notation is now equal to 1
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 107 is 5
Multiplying this coefficient by our original value, we get: 5 * 8 = 40
Add our new value to our running total, we get:
64 + 40 = 104
This is <= 107, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 104
Our octal notation is now equal to 15
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 107 is 3
Multiplying this coefficient by our original value, we get: 3 * 1 = 3
Add our new value to our running total, we get:
104 + 3 = 107
This = 107, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 107
Our octal notation is now equal to 153
