Convert `(273)_8` to binary.

Answer

To convert the octal number \( (273)_8 \) to binary, we can follow these steps:

### Step 1: Understand the octal number system
The octal number system is base 8, which means it uses digits from 0 to 7. Each digit represents a power of 8.

### Step 2: Convert each octal digit to binary
Each octal digit can be directly converted to a 3-digit binary number since \( 2^3 = 8 \). We will convert each digit of \( 273_8 \) to its binary equivalent.

- **Convert 2 (octal) to binary**:
- \( 2 \) in binary is \( 010 \).

- **Convert 7 (octal) to binary**:
- \( 7 \) in binary is \( 111 \).

- **Convert 3 (octal) to binary**:
- \( 3 \) in binary is \( 011 \).

### Step 3: Combine the binary equivalents
Now, we will combine the binary representations of each digit together in the same order they appear in the octal number.

- For \( 2 \): \( 010 \)
- For \( 7 \): \( 111 \)
- For \( 3 \): \( 011 \)

Combining these gives us:
\[ 010 \, 111 \, 011 \]

### Step 4: Final binary representation
Thus, the binary representation of the octal number \( (273)_8 \) is:
\[ (010111011)_2 \]

### Summary
The octal number \( (273)_8 \) converts to binary as \( (010111011)_2 \).

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