Convert 263 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 >= 263
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 263
Since 512 is greater than 263, 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 263 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 <= 263, 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 263 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
256 + 8 = 264
This is > 263, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our octal notation is now equal to 40
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 263 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
256 + 7 = 263
This = 263, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 263
Our octal notation is now equal to 407
