Hexadecimal to Octal Conversion Explained

Converting a number from one base to another is a fundamental concept in digital electronics and computer science. To convert a hexadecimal number to an octal number, it is generally easiest to first convert the hexadecimal number to its binary equivalent, and then convert the binary equivalent to the octal number.

Understanding the Conversion Process

The process involves two main steps:

1. Convert the given hexadecimal number to binary.
2. Convert the binary number obtained in step 1 to octal.

Step 1: Convert Hexadecimal to Binary

Each hexadecimal digit can be represented by exactly four binary digits (bits). Let's convert each digit of the hexadecimal number \( (236)_{16} \) into its 4-bit binary equivalent.

Combining these binary equivalents, we get:

\( (236)_{16} = (0010 \ 0011 \ 0110)_2 \)

We can remove the leading zeros if they don't precede a '1', but for grouping in the next step, it's useful to keep them to ensure the total number of bits is a multiple of 3. So, the binary representation is \( (001000110110)_2 \).

Step 2: Convert Binary to Octal

Each octal digit can be represented by exactly three binary digits. To convert the binary number \( (001000110110)_2 \) to octal, we group the binary digits into sets of three, starting from the rightmost digit. If the leftmost group doesn't have three digits, we pad it with leading zeros.

Our binary number is \( 001000110110 \). Let's group it:

\( 001 \ 000 \ 110 \ 110 \)

Now, convert each 3-bit group into its octal equivalent:

Combining these octal digits, we get:

\( (001000110110)_2 = (1066)_8 \)

Final Octal Result

Therefore, the octal equivalent of the hexadecimal number \( (236)_{16} \) is \( (1066)_8 \).