Octal to Binary Conversion Explained

Converting an octal number to binary involves replacing each octal digit with its equivalent 3-bit binary representation. This is because each octal digit (0-7) can be uniquely represented by three binary digits (000-111).

Step-by-Step Conversion

1. Identify Octal Digits: The octal number provided is $456$. The individual digits are 4, 5, and 6.
2. Find 3-Bit Binary Equivalents: Convert each octal digit into its 3-bit binary form:
   • Octal digit $4$ corresponds to binary $100$.
   • Octal digit $5$ corresponds to binary $101$.
   • Octal digit $6$ corresponds to binary $110$.
3. Combine Binary Groups: Concatenate the 3-bit binary representations obtained in the previous step, maintaining the original order.

   Combining $100$, $101$, and $110$ gives $100101110$.

Final Binary Equivalent

Thus, the binary equivalent of the octal number 456 is 100101110.