If `(11011)_(2), = (_______)_(10)`, then number in the blank space is

Options

A. 33
B. 22
C. 27
D. 30

Explanation

To convert the binary number \( (11011)_2 \) to decimal \( (x)_{10} \), we follow these steps:

### Step 1: Write down the binary number and its positional values.
The binary number is \( 11011 \). Each digit represents a power of 2, starting from the rightmost digit which is \( 2^0 \).

### Step 2: Assign powers of 2 to each digit.
- The rightmost digit (1) is \( 2^0 \)
- The next digit (1) is \( 2^1 \)
- The next digit (0) is \( 2^2 \)
- The next digit (1) is \( 2^3 \)
- The leftmost digit (1) is \( 2^4 \)

So we have:
- \( 1 \times 2^4 \)
- \( 1 \times 2^3 \)
- \( 0 \times 2^2 \)
- \( 1 \times 2^1 \)
- \( 1 \times 2^0 \)

### Step 3: Calculate the value of each term.
- \( 1 \times 2^4 = 1 \times 16 = 16 \)
- \( 1 \times 2^3 = 1 \times 8 = 8 \)
- \( 0 \times 2^2 = 0 \times 4 = 0 \)
- \( 1 \times 2^1 = 1 \times 2 = 2 \)
- \( 1 \times 2^0 = 1 \times 1 = 1 \)

### Step 4: Add the values together.
Now we add these values:
\[ 16 + 8 + 0 + 2 + 1 = 27 \]

### Conclusion:
Thus, the decimal equivalent of the binary number \( (11011)_2 \) is \( (27)_{10} \).

### Final Answer:
\[ (11011)_2 = (27)_{10} \]

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