Number conversions have a great importance in computer science. Octal to decimal conversion is also very important there.
Not only for computer science but also for general students who want to learn about computer science and number system must have to know about different types of number conversions.
Keeping that in mind, in this post I am going to teach you all the details about number conversion from octal to decimal. We will also post everything about number conversion step by step in this site.
The thing is that, octal is an eight based number where we can use 8 digits from 0 to 7 to write any number. On the other hand in decimal, there are 10 digits to write any number which starts from 0 and end at 9.
The concept of base is very important, when we convert a number from one to another. If you have not the idea about number systems then please see our following post first.
Number system and conversion of number system of binary, octal, decimal and hexadecimal.
Ok, now you have the basic idea about all the well known number system. So you will now be able to understand everything which I will discussed here.
We will use two rules for converting a number from octal to decimal here as like as other number system conversion. We will convert separately the integer number and fraction number.
To convert a number from octal to decimal we will start with the integer number first. Then we will learn about the fraction number. So, let’s get started.
Rules for integer part:
We can divided the rules for integer part for converting a number from octal to decimal by following two sections.
- Determine the positional value of every digit of octal number. Multiply every digit by 8^{0}, 8^{1}, 8^{2}, 8^{3}, 8^{4} and so one from right to left.
- Add all these values which will be the equivalent decimal number.
Now, let’s see an example conversion for implement these two rules. Here, we will convert a octal integer to decimal integer.
Example : Conversion of (16512)_{8} to equivalent decimal number.
Here in the solution we have multiplied every digits by the positional value of octal number system. After adding them, we will get the equivalent decimal value. Just see bellow;
Solution :
= 1 × 8^{4} + 6 × 8^{3} + 5 × 8^{2} + 1 × 8^{1} + 2 × 8^{0}
= 4096 + 3072 + 320 + 8 + 2
= 7498
So, we can tell that the decimal equivalent of octal number 16512 is 7498. You can convert any integer octal number by these rules to the equivalent decimal integer number. Now, you should try this for different numbers.
Now, we will see another method to convert this number from octal to decimal. Obviously you can use any one of them and both will be the correct method.
After converting the number by both the method we have got the result in decimal is 7498. So, use your favorite method from the above two method. to convert a number from octal to decimal.
Now, let’s head over the conversion of fraction octal number to equivalent decimal number. For this we have to learn two rules which is given bellow in the list.
Rules for fraction part of the number:
- Determine the positional value of every digit of octal fraction number multiplying every digit by 8^{-1}, 8^{-2}, 8^{-3}, 8^{-4} and so one from left to right.
- Add all these values which will give the equivalent value of fractional octal number to decimal number.
You may have not understand anything by these two rules. Don’t worry, I will make it more easy by giving an example. Let’s see the following example to get a clear idea about octal to decimal conversion for a fraction number.
Example : Conversion of (0.145)_{8} to equivalent decimal number.
Here, we will also use the same concept for converting this octal number to equivalent decimal number. What we have to do is just multiply every digit by their positional value and then add them.
Solution :
(0.145)_{8}
= 1 × 8^{-1} + 4 × 8^{-2} + 5 × 8^{-3}
= 0.125 + 0.0588 + 0.0098
= 0.1936
Note: Here, we have taken everything from 3 digits after radix point. You can check more if wnat.
So, we have got the result in decimal is 0.1936
So, I hope guy’s, now everything is clear to you that how you can convert a number from octal to decimal using general rules of conversion. Now, you should practice this for different numbers.
But it is not impossible to remain some doubt about this conversion. Keeping that in mind, I have put a full example of converting a number from octal to decimal here.
This complete example will really be very helpful to you to understand the topics. So, let’s see the example bellow.
Example : Conversion of (10512.145)_{8} to its equivalent decimal number.
Solution :
We will convert its integer part first and then go to the fraction part. You can follow our given rules for this purpose. Let’s try to understand the example given bellow;
= 1 × 8^{4} + 0 × 8^{3} + 5 × 8^{2} + 1 × 8^{1} + 2 × 8^{0}
= 4096 + 0 + 320 + 8 + 2
= 4426
Again applying the second method to convert this number from octal to decimal we get the following figure.
According to our given rules, the conversion of the fraction part of this number will be as like as following.
(0.145)_{8}
= 1 × 8^{-1} + 4 × 8^{-2} + 5 × 8^{-3}
= 0.125 + 0.0588 + 0.0098
= 0.1936
Note: We have took 3 digits after radix point here in this example.
However, after converting the number from octal to its equivalent decimal we have got (4426.1936)_{10} .
Now, you should try to convert some other number too to get the clear conception about this topics. You can convert any octal number to its equivalent decimal number by this rules.
Hope, this guide is able to give you a good idea about this conversion. I have made this post very easy for everyone. Hope, you have understand everything.
If you find any unexpected mistakes or have any doubt yet, then please let us know in the comment box bellow. We are highly interested to here about our website from you.
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