In this post, we will learn the method used to convert a given integer octal number to its equivalent in the binary number system
The octal number system has a base of 8 i.e. the number of digits in the octal number system is eight(8) starting from 0 to 7.
- The highest digit in the octal number system is (7)8, from the number system conversion table we can see that (111)2 is the binary equivalent of the highest octal digit and three binary digits(bits) are required to represent the highest octal digit.
- In the octal to binary conversion method, we will convert each digit from the given octal number into three bit binary number starting from the right most octal digit(LSD) to the left most digit(MSD) and at the end combine each three bit binary number to form the binary equivalent of given octal number.
- The steps involved in the octal to binary conversion is explained with example below:
Example-1: Convert octal number (375)8 to binary number (?)2
Step 1:
Write down each digit from the given octal number leaving some space between each octal digit as shown below
Octal Number -> 3 7 5
Step 2:
If you have memorized the binary equivalents of all the octal digits this step becomes very easy, otherwise you can still refer the conversion table to find the binary equivalents of each octal digit.Represent each octal digit with its binary equivalent as shown below
We know that,
Binary equivalent of octal digit 3 is 011
Binary equivalent of octal digit 7 is 111
Binary equivalent of octal digit 5 is 101
Write down the three bit number below each octal digit as shown below:
Octal Number -> 3 7 5
↓ ↓ ↓
Binary Number -> 011 111 101
Group the binary equivalents of each octal digit starting from right most digit to obtain the complete binary equivalent of the given octal number.
We know that,
Binary equivalent of octal digit 6 is 110
Binary equivalent of octal digit 3 is 011
Binary equivalent of octal digit 4 is 100
Binary Number -> 011 111 101
Step 3:
Group the binary equivalents of each octal digit starting from right most digit to obtain the complete binary equivalent of the given octal number.
Hence, the binary equivalent of the given octal number is (11111101)2
Example-2: Convert octal number (634)8 to binary number (?)2
Step 1:
Write down each digit from the given octal number as shown below
Octal Number -> 6 3 4
Step 2:
Represent each octal digit with its binary equivalent as shown belowWe know that,
Binary equivalent of octal digit 6 is 110
Binary equivalent of octal digit 3 is 011
Binary equivalent of octal digit 4 is 100
Write down the three bit binary equivalents below each octal digit as shown below:
Octal Number -> 6 3 4
↓ ↓ ↓
Binary Number -> 110 011 100
Group the binary equivalents of each octal digit starting from right most digit to obtain the complete binary equivalent of the given octal number.
Binary Number -> 110 011 100
Step 3:
Group the binary equivalents of each octal digit starting from right most digit to obtain the complete binary equivalent of the given octal number.