The conversion of one number system to another, as we explained earlier, is done to simplify computer programming or interpreting of data.
Octal to Binary
For some computers to accept octal data, the octal digits must be converted to binary. This process is the reverse of binary to octal conversion.
To convert a given octal number to binary, write out the octal number in the following format. We will convert octal 5678:
Next, below each octal digit write the corresponding three-digit binary-coded octal equivalent:
Solution: 5678 equals 101 110 1112
Remove the conversion from the format:
As you gain experience, it may not be necessary to use the block format.
An octal fraction (.1238) is converted in the same manner, as shown below:
Solution: .1238 equals .0010100112
Apply these principles to convert mixed numbers as well.
Convert 32.258 to binary:
Solution: 32.258 equals 011010.0101012
Convert the following numbers to binary: