To convert an octal number to its hexadecimal equivalent, you can follow a two-step process: first, convert the octal number to binary, and then convert the binary number to hexadecimal.

Understanding the Number Systems

Octal numbers are base-8, which means they can include digits from $0$ to $7$. In contrast, hexadecimal numbers are base-16 and utilize digits from $0$ to $9$ as well as letters from $A$ to $F$. Lastly, binary numbers are base-2, consisting solely of the digits $0$ and $1$.

Step 1: Convert Octal to Binary

The first step involves converting the octal number to binary. Each digit in an octal number can be represented by a three-digit binary equivalent. For instance, the octal digit $7$ corresponds to the binary $111$, while the octal digit $2$ corresponds to $010$.

For example, if you have the octal number $72$, you would convert it to binary by substituting each digit with its binary counterpart. Thus, $72$ in octal translates to:

As a result, the octal number $72$ becomes the binary number $111010$.

Step 2: Convert Binary to Hexadecimal

The next step is to convert the binary number to hexadecimal. Each hexadecimal digit can be represented by a four-digit binary number. For example, the hexadecimal digit $F$ is represented as $1111$ in binary, and the digit $2$ is represented as $0010$.

To convert from binary to hexadecimal, group the binary digits into sets of four, starting from the right. If there are not enough digits to form a complete group of four, you can add leading zeros.

Continuing with our previous example, the binary number $111010$ can be grouped as follows:

Now, we can convert each group to its hexadecimal equivalent:

• The binary group $0011$ corresponds to $3$ in hexadecimal.
• The binary group $1010$ corresponds to $A$ in hexadecimal.

Thus, the hexadecimal equivalent of the octal number $72$ is $3A$.

Summary

In summary, the process of converting an octal number to hexadecimal involves two conversions: first from octal to binary, and then from binary to hexadecimal. While this may seem a bit complex initially, it becomes easier with practice. This skill is particularly useful for those studying computer science, as these number systems frequently appear in computing and programming contexts.