How do you convert an octal number to its binary equivalent?

To convert an octal number to binary, each octal digit is replaced by its corresponding three-digit binary number.

Octal numbers are base-8 numbers, meaning they use digits from 0 to 7. Binary numbers, on the other hand, are base-2, using only 0 and 1. To convert an octal number to binary, you simply replace each octal digit with its corresponding three-digit binary number.

Here's a step-by-step guide on how to do it:

1. Write down the octal number and identify each digit. For example, if you have the octal number 345, the digits are 3, 4, and 5.

2. Convert each octal digit to its binary equivalent using the following table:

Octal: 0 1 2 3 4 5 6 7
Binary: 000 001 010 011 100 101 110 111

So, for our example, 3 in octal is 011 in binary, 4 is 100, and 5 is 101.

3. Write down the binary equivalents in the same order as the octal digits. So, the octal number 345 becomes the binary number 011100101.

Remember, each octal digit corresponds to exactly three binary digits. This is because the largest digit in octal (7) requires three binary digits to represent (111). So, even if the binary equivalent of an octal digit can be represented in fewer than three binary digits (like 2 in octal is 10 in binary), you should always write it as a three-digit binary number (010) for consistency.

This method is straightforward and easy to use, but it does require you to memorise or have access to the conversion table. With practice, you'll be able to convert between octal and binary numbers quickly and accurately.