# Octal to Binary

Octal to Binary tool

## Converting Octal to Binary

Have you ever been stuck trying to figure out how to convert octal to binary? Don't worry, you're not alone. Converting between number systems is a common challenge for many people, but it doesn't have to be daunting. In this blog post, we'll walk you through the step-by-step process of converting octal to binary.

**First**, let's clarify what octal and binary are. Octal is a base-8 numbering system, meaning it uses eight distinct digits (0-7). Binary, on the other hand, is a base-2 numbering system, meaning it only uses two digits (0 and 1). To convert from octal to binary, we'll need to convert each octal digit to its binary equivalent.

To do this, we can use a table of octal and binary equivalents. Here's a simple one to get you started:

Octal | Binary

-----|------

0 | 000

1 | 001

2 | 010

3 | 011

4 | 100

5 | 101

6 | 110

7 | 111

To convert an octal digit to binary, simply look it up in the left column of the table and write down the corresponding binary number from the right column. For example, if we want to convert the octal number 762 to binary, we would use the table to write down the binary equivalents of each digit:

7 6 2

111 110 010

Then, we simply concatenate the binary equivalents to get the final binary representation of the octal number. In this case, the binary equivalent of 762 is 111110010.

What if we have an octal number with a decimal point? In that case, we treat the part before the decimal point and the part after the decimal point separately. We convert the part before the decimal point to binary as usual, and then convert the part after the decimal point by using the table above to convert each digit to its binary equivalent. We then combine the two binary representations with the decimal point in the appropriate place.

For example, let's convert the octal number 7.65 to binary. We first convert the part before the decimal point (7) to binary by looking it up in our table and writing down the binary equivalent, which is 111. We then convert the part after the decimal point (65) by looking up each digit in the table and writing down the corresponding binary number:

6 5

110 101

We then combine the two parts with the decimal point in the appropriate place to get the final binary representation of 7.65, which is 111.110101.

Converting octal to binary is not as difficult as it might seem. By using a table of octal and binary equivalents and following the steps outlined above, you can easily convert any octal number to binary. With this knowledge, you can feel confident in working with numbers in different number systems and continue to expand your understanding of mathematics.