Convert 287 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 >= 287
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 287
Since 512 is greater than 287, 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 287 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 <= 287, 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 287 is 3
Multiplying this coefficient by our original value, we get: 3 * 8 = 24
Add our new value to our running total, we get:
256 + 24 = 280
This is <= 287, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 280
Our octal notation is now equal to 43
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 287 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
280 + 7 = 287
This = 287, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 287
Our octal notation is now equal to 437
