Convert 120 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 >= 120
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 120
Since 512 is greater than 120, 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 120 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 <= 120, 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 120 is 7
Multiplying this coefficient by our original value, we get: 7 * 8 = 56
Add our new value to our running total, we get:
64 + 56 = 120
This = 120, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 120
Our octal notation is now equal to 17
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 120 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
120 + 1 = 121
This is > 120, so we assign a 0 for this digit.
Our total sum remains the same at 120
Our octal notation is now equal to 170
