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

To convert an octal number to its hexadecimal equivalent, first convert the octal number to binary, then convert the binary to hexadecimal.

To understand this process, let's break it down step by step. Octal numbers are base-8 numbers, meaning they use digits from 0 to 7. Hexadecimal numbers are base-16 numbers, using digits from 0 to 9 and letters from A to F. Binary numbers are base-2, using only 0 and 1.

The first step is to convert the octal number to binary. Each digit in an octal number can be represented by a three-digit binary number. For example, the octal digit 7 is 111 in binary, and the octal digit 2 is 010 in binary. So, if you have an octal number like 72, you would convert it to binary by replacing each digit with its binary equivalent, resulting in 111 010.

The next step is to convert the binary number to hexadecimal. Each digit in a hexadecimal number can be represented by a four-digit binary number. For example, the hexadecimal digit F is 1111 in binary, and the hexadecimal digit 2 is 0010 in binary. To convert from binary to hexadecimal, group the binary digits into sets of four, starting from the right. If you don't have enough digits to make a group of four, you can add zeros to the left. Then, replace each group with its hexadecimal equivalent.

Using our previous example, the binary number 111 010 would be grouped into 0111 0010. The binary group 0111 is 7 in hexadecimal, and the binary group 0010 is 2 in hexadecimal. So, the hexadecimal equivalent of the octal number 72 is 72.

Remember, this process involves two conversions: octal to binary, then binary to hexadecimal. It may seem a bit complex at first, but with practice, it becomes easier. It's a useful skill to have, especially for those studying computer science, as these number systems are often used in computing and programming.