The decimal representation of the number `(1011)_(2)` in binary system is:

Options

A. 5
B. 7
C. 9
D. 11

Answer

To convert the binary number \( (1011)_2 \) to its decimal representation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Binary Number**: The given binary number is \( 1011 \).

2. **Write Down the Powers of 2**: Starting from the rightmost digit (which is the least significant bit), write down the powers of 2 for each position:
- The rightmost digit (1st position) corresponds to \( 2^0 \)
- The next digit (2nd position) corresponds to \( 2^1 \)
- The next digit (3rd position) corresponds to \( 2^2 \)
- The leftmost digit (4th position) corresponds to \( 2^3 \)

So, we have:
- \( 2^3 \) for the leftmost 1
- \( 2^2 \) for the 0
- \( 2^1 \) for the 1
- \( 2^0 \) for the rightmost 1

3. **Multiply Each Bit by Its Corresponding Power of 2**:
- The leftmost bit (1) contributes: \( 1 \times 2^3 = 1 \times 8 = 8 \)
- The next bit (0) contributes: \( 0 \times 2^2 = 0 \times 4 = 0 \)
- The next bit (1) contributes: \( 1 \times 2^1 = 1 \times 2 = 2 \)
- The rightmost bit (1) contributes: \( 1 \times 2^0 = 1 \times 1 = 1 \)

4. **Add All the Contributions Together**:
- Now, we sum all the contributions:
\[ 8 + 0 + 2 + 1 = 11 \]

5. **Conclusion**: Therefore, the decimal representation of the binary number \( (1011)_2 \) is \( 11 \).

### Final Answer:
The decimal representation of \( (1011)_2 \) is \( 11 \).

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