How to Convert Octal to Binary.

The digit expansion method.

To convert an octal number (base-8) to a binary number (base-2), you perform the reverse of the grouping method: you take each individual digit of the octal number and expand it into its exact 3-bit binary representation.

This method is extremely straightforward and doesn't require decimal calculation. Each octal digit corresponds to a specific 3-digit binary code, which can be concatenated to produce the final binary value.

Octal to binary steps by hand.

1. Start with your octal value (e.g. 345).
2. Take each digit separately: 3, 4, and 5.
3. Convert each digit to its 3-bit binary equivalent:
   • 3 ➔ 011
   • 4 ➔ 100
   • 5 ➔ 101
4. Combine the binary groups in order: 011 + 100 + 101 = 011100101 (or simply 11100101).