Convert 275 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 >= 275
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 275
Since 512 is greater than 275, 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 275 is 4
Multiplying this coefficient by our original value, we get: 4 * 64 = 256
Add our new value to our running total, we get:
0 + 256 = 256
This is <= 275, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 256
Our octal notation is now equal to 4
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 275 is 2
Multiplying this coefficient by our original value, we get: 2 * 8 = 16
Add our new value to our running total, we get:
256 + 16 = 272
This is <= 275, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 272
Our octal notation is now equal to 42
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 275 is 3
Multiplying this coefficient by our original value, we get: 3 * 1 = 3
Add our new value to our running total, we get:
272 + 3 = 275
This = 275, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 275
Our octal notation is now equal to 423
