What is an Octal Number?
The easiest way to understand an octal number is to compare it to something you already know -- a decimal number.
As you know, a decimal number uses the base-ten system for counting and expressing value. It's called "base 10" because it uses ten numeric characters (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to count and express values.
On the other hand, the octal number system uses the base-8 method for counting and expressing value. It's called "base 8" because it uses eight numeric characters to count and express value. The eight octal numeric characters are 0, 1, 2, 3, 4, 5, 6, and 7.
Now, since we are looking to convert a base 8 number into a base 10 number, let's compare the base 10 place values to the place values in a base 8 number system:
How to Convert Octal to decimal
To help you to understand how to convert octal to decimal, it may help to look at how we translate the value of a decimal number. Let's use the decimal number 1234 (123410, or one-thousand, two-hundred and thirty-four) as an example:Translating the Value of a Decimal (base 10) Number
With the above base 10 translation in mind, here is how you would convert the base 8 number 1234 (12348) into a base 10 number:Converting an Octal (base 8) to a Decimal (base 10)
Adding the values of line D, we get the base 10 number of 668. In other words, the number 12348 coverts to the number 66810.
As you can see, converting an octal number to a decimal number is a simple process of identifying the place value of each digit, multiplying each digit by its place value, and then adding up all of the products.
Or, if the octal number doesn't have a radix point, there is a second method you can use to convert octal numbers to decimal numbers.Successive Duplication Method
To convert an octal number without a decimal point to a decimal number using the successive duplication method, add "0." to the front of the number and then perform the following steps:
- Double the value to the left side of the decimal point and place the result on the next line, right-aligned to one digit right of the decimal point.
- Subtract the doubled value from the digits above and to the left of it and place the results on the next line, moving the decimal point 1 place to the right.
- Drop the remaining digits to the next row unchanged.
- Repeat steps 1-3 for as long as digits remain on the right side of the decimal point.
The display below shows how to use this method to convert the earlier example (1234) to Decimal: