Binary to octal number conversion is very well known among each students today as both binary and octal are two of the most popular number system we use in computer technology. Before going ahead let’s learn a little bit about those two number system.
Binary is a two based number system where we can only use either 0 or 1 to write any number. This number system plays a very important role in computer science as the computer can only understand binary digits.
On the other hand, octal is an eight based number system where the digits are 0, 1, 2, 3, 4, 5, 6 and 7. Octal is also a popular number system. We can convert one to another of this two number system.
However, in this post I will discuss almost everything about binary to octal conversion. That means we will convert a number from binary to octal here.
To convert any binary number to the equivalent octal number we have to learn two methods. One is for fraction part where another is for integer part.
We will learn each conversion that means conversion of integer part and conversion of fraction part here in this post. So, let’s go ahead with the rules for integer part to convert a number from binary to octal.
Table of Contents
Binary to octal number conversion
Rules for integer portion:
No matter if you can’t understand these rules. It will clear if you see the following example of convert an integer number from binary to octal. Let’s head over that.
Example : Conversion of (1110101011)2 to equivalent octal number.
This conversion is very easy. We will take every 3 digits from right to left and then take their equivalent octal value instead of them.
We will take necessary zeros at the leftmost side of the binary number. Let’s see the figure bellow;
We can also ignore unnecessary zeros from left, when we convert an integer from binary to octal. This rules works as our generally used decimal number where we can write 54 instead of 054 and 98 instead of 098.
In the above conversion we have got 1653 as the octal equivalent of the given binary number. By using the same rules you can convert any binary number to equivalent octal number.
Obviously you should try that but now we have to see some other rules for fraction part of binary number.
The rules for fraction number to convert from binary to octal is almost same as the conversion of integer part. Let’s see the rules bellow;
Rules for fraction number :
Although the concept is same as the conversion of integer part we will also see an example of converting a fraction number from binary to octal bellow.
Example : Conversion of (0.10001000111)2 to equivalent octal number.
Here also we will take each 3 digits of binary number from left to right. We can take necessary zeros at the rightmost side to fill up the last pair of 3 bits. See bellow figure.
Zeros at right side do not affect the value of binary number when we convert the fraction part of binary to octal number. This rules works as our generally used decimal number that we can write 0.22 instead of 0.220 and 0.343 instead of 0.34300
So, in the above figure, we have got 0.4216 at octal when we convert the given fraction binary number to equivalent octal number. You can convert any number by this rule.
Although it is totally up to you that how much you will practice to make the conversion from binary to octal easy to you. But here we will see one more conversion to give you some more example of such conversion.
Here, we will see a full example to convert a number from binary to octal. We will use both the rules for converting fraction part as well as integer part at a single figure. Let’s see the example bellow;
Example : Conversion of (10010111.11001)2 to equivalent octal number.
To convert this binary number to its equivalent octal number we can convert whole number by a single rule which will apply at both it’s integer part and fraction part.
We will ignore zeros at left side of integer and right side of fraction part and take necessary zeros at left side of the integer and right side of the fraction part.
You can also convert its integer and fraction part separately. But we have the chance to convert the whole number at a time as the rules for integer and fraction number are almost same.
Now, let’s go to the conversion method bellow.
Now, we get the octal equivalence of given binary number is (227.62)8 . You can convert any binary number to its equivalent octal number by these rules which we have discussed here.
To become an expert at number conversion you have to practice more and more by taking different binary number. Try to convert them using the given rules here.
It is sure that you will learn everything related to binary to octal conversion one day.
However, I already have told all the rules for converting a number from binary to octal in this post. I have made it very easy to all that you can understand easily.
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