Convert 80 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 >= 80
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 80
Since 512 is greater than 80, we use 1 power less as our starting point which equals 2
Work backwards from a power of 2
We start with a total sum of 0:
The highest coefficient less than 7 we can multiply this by to stay under 80 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 <= 80, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our octal notation is now equal to 1
The highest coefficient less than 7 we can multiply this by to stay under 80 is 2
Multiplying this coefficient by our original value, we get: 2 * 8 = 16
Add our new value to our running total, we get:
64 + 16 = 80
This = 80, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 80
Our octal notation is now equal to 12
The highest coefficient less than 7 we can multiply this by to stay under 80 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
80 + 1 = 81
This is > 80, so we assign a 0 for this digit.
Our total sum remains the same at 80
Our octal notation is now equal to 120