Convert 66 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 >= 66
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 66
Since 512 is greater than 66, 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 66 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 <= 66, 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 66 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
64 + 8 = 72
This is > 66, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our octal notation is now equal to 10
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 66 is 2
Multiplying this coefficient by our original value, we get: 2 * 1 = 2
Add our new value to our running total, we get:
64 + 2 = 66
This = 66, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 66
Our octal notation is now equal to 102
Final Answer
Test Your Knowledge?
- Binary means base _?
- Octal means base _?
- Hexadecimal means base __?
What is the Answer?
How does the Base Change Conversions Calculator work?
This calculator has 3 inputs.
What 3 formulas are used for the Base Change Conversions Calculator?
Octal = Base 8
Hexadecimal = Base 16
What 6 concepts are covered in the Base Change Conversions Calculator?
- base
- base change conversions
- binary
- Base 2 for numbers
- conversion
- a number used to change one set of units to another, by multiplying or dividing
- hexadecimal
- Base 16 number system
- octal
- base 8 number system
