Convert 206 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 >= 206
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 206
Since 512 is greater than 206, 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 206 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 <= 206, 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 206 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
192 + 8 = 200
This is <= 206, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 200
Our octal notation is now equal to 31
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 206 is 6
Multiplying this coefficient by our original value, we get: 6 * 1 = 6
Add our new value to our running total, we get:
200 + 6 = 206
This = 206, so we assign our outside coefficient of 6 for this digit.
Our new sum becomes 206
Our octal notation is now equal to 316
