Convert 178 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 >= 178
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 178
Since 512 is greater than 178, 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 178 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 <= 178, 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 178 is 6
Multiplying this coefficient by our original value, we get: 6 * 8 = 48
Add our new value to our running total, we get:
128 + 48 = 176
This is <= 178, so we assign our outside coefficient of 6 for this digit.
Our new sum becomes 176
Our octal notation is now equal to 26
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 178 is 2
Multiplying this coefficient by our original value, we get: 2 * 1 = 2
Add our new value to our running total, we get:
176 + 2 = 178
This = 178, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 178
Our octal notation is now equal to 262
