Convert 217 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 >= 217
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 217
Since 512 is greater than 217, 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 217 is 3
Multiplying this coefficient by our original value, we get: 3 * 64 = 192
Add our new value to our running total, we get:
0 + 192 = 192
This is <= 217, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 192
Our octal notation is now equal to 3
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 217 is 3
Multiplying this coefficient by our original value, we get: 3 * 8 = 24
Add our new value to our running total, we get:
192 + 24 = 216
This is <= 217, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 216
Our octal notation is now equal to 33
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 217 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
216 + 1 = 217
This = 217, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 217
Our octal notation is now equal to 331
