Convert 133 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 >= 133
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 133
Since 512 is greater than 133, 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 133 is 2
Multiplying this coefficient by our original value, we get: 2 * 64 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This is <= 133, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 128
Our octal notation is now equal to 2
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 133 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
128 + 8 = 136
This is > 133, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our octal notation is now equal to 20
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 133 is 5
Multiplying this coefficient by our original value, we get: 5 * 1 = 5
Add our new value to our running total, we get:
128 + 5 = 133
This = 133, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 133
Our octal notation is now equal to 205
