Question

How to convert 24 octal to binary?

Answer 1

To convert an octal number to binary, follow these steps:

### Step-by-Step Conversion from Octal to Binary:
1. **Understand the octal system**: The octal system (base-8) uses digits from 0 to 7. Each octal digit can be represented by a group of 3 binary digits (since \(2^3 = 8\)).

2. **Separate each digit of the octal number**: For the octal number 24, break it down into its individual digits.
   - 2
   - 4

3. **Convert each octal digit to binary**:
   Each octal digit can be directly converted to a 3-bit binary number:
   - The octal digit `2` is \( 010_2 \) (binary).
   - The octal digit `4` is \( 100_2 \) (binary).

4. **Write the binary equivalents together**:
   Combine the binary values of each octal digit:
   - Octal 24 becomes \( 010 \ 100_2 \).

5. **Result**: The binary equivalent of the octal number 24 is \( 010100_2 \), or simply \( 10100_2 \) (since leading zeros can be dropped).

### Final Answer:
The octal number \( 24_8 \) is equivalent to the binary number \( 10100_2 \).

Answer 2

To convert an octal (base-8) number to a binary (base-2) number, you can follow these steps. Let's use the octal number `24` as an example.

### Steps for Conversion:

1. **Convert Octal Digits to Binary:**
   Each digit in an octal number can be directly converted to a 3-bit binary equivalent because octal is base-8, and binary is base-2. The number 8 in base-8 is \(2^3\) in base-2, so each octal digit corresponds to exactly three binary digits.

   Here are the conversions for each digit:
   - Octal `0` → Binary `000`
   - Octal `1` → Binary `001`
   - Octal `2` → Binary `010`
   - Octal `3` → Binary `011`
   - Octal `4` → Binary `100`
   - Octal `5` → Binary `101`
   - Octal `6` → Binary `110`
   - Octal `7` → Binary `111`

2. **Convert Each Octal Digit of `24` to Binary:**
   - The octal digit `2` converts to binary `010`.
   - The octal digit `4` converts to binary `100`.

3. **Combine the Binary Digits:**
   Place the binary representations of each digit next to each other, preserving their order:
   - For octal `24`, you get: `010 100`.

4. **Remove Leading Zeros (if necessary):**
   In this case, the binary number `010100` doesn't have leading zeros beyond what is necessary for the place values, so it remains as `010100`.

### Final Binary Representation:
The binary equivalent of the octal number `24` is `010100`.

If you prefer, you can also remove leading zeros to simplify it further to `10100`, but both forms are technically correct, with `010100` being the more complete representation that retains the same number of digits as in the conversion process.