Convert `(16504)_8` to binary .

Answer

To convert the octal number \( (16504)_8 \) to binary, we can follow these steps:

### Step 1: Understand the octal to binary conversion
Each digit in an octal number can be represented by a 3-bit binary equivalent. The octal system is base 8, and each digit can take values from 0 to 7.

### Step 2: Write down the octal number
The octal number we have is \( 16504_8 \).

### Step 3: Convert each octal digit to binary
Now, we will convert each digit of the octal number to its 3-bit binary equivalent:

- The digit \( 1 \) in octal is \( 001 \) in binary.
- The digit \( 6 \) in octal is \( 110 \) in binary.
- The digit \( 5 \) in octal is \( 101 \) in binary.
- The digit \( 0 \) in octal is \( 000 \) in binary.
- The digit \( 4 \) in octal is \( 100 \) in binary.

### Step 4: Combine the binary equivalents
Now we will combine all the binary equivalents together:

- From \( 1 \): \( 001 \)
- From \( 6 \): \( 110 \)
- From \( 5 \): \( 101 \)
- From \( 0 \): \( 000 \)
- From \( 4 \): \( 100 \)

Putting them together, we get:
\[ 001 \, 110 \, 101 \, 000 \, 100 \]

### Step 5: Write the final binary number
Thus, the binary representation of \( (16504)_8 \) is:
\[ (001110101000100)_2 \]

### Final Answer
The binary equivalent of \( (16504)_8 \) is \( (001110101000100)_2 \).

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