Convert 127 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 >= 127
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 127
Since 512 is greater than 127, 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 127 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 127, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our octal notation is now equal to 1
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 127 is 7
Multiplying this coefficient by our original value, we get: 7 * 8 = 56
Add our new value to our running total, we get:
64 + 56 = 120
This is <= 127, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 120
Our octal notation is now equal to 17
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 127 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
120 + 7 = 127
This = 127, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 127
Our octal notation is now equal to 177
