If `(11101011)_(2)` is converted to decimal system, then the resulting number is:

Options

A. 235
B. 175
C. 160
D. 126

Answer

To convert the binary number \( (11101011)_2 \) to its decimal equivalent, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Binary Number**:
The binary number given is \( 11101011 \).

2. **Assign Powers of 2**:
Each digit in the binary number corresponds to a power of 2, starting from the rightmost digit (which is \( 2^0 \)) to the leftmost digit. The powers will be:
- \( 1 \times 2^7 \)
- \( 1 \times 2^6 \)
- \( 1 \times 2^5 \)
- \( 0 \times 2^4 \)
- \( 1 \times 2^3 \)
- \( 0 \times 2^2 \)
- \( 1 \times 2^1 \)
- \( 1 \times 2^0 \)

3. **Calculate Each Term**:
- \( 1 \times 2^7 = 128 \)
- \( 1 \times 2^6 = 64 \)
- \( 1 \times 2^5 = 32 \)
- \( 0 \times 2^4 = 0 \)
- \( 1 \times 2^3 = 8 \)
- \( 0 \times 2^2 = 0 \)
- \( 1 \times 2^1 = 2 \)
- \( 1 \times 2^0 = 1 \)

4. **Sum All the Values**:
Now, we will add all the calculated values together:
\[ 128 + 64 + 32 + 0 + 8 + 0 + 2 + 1 = 235 \]

5. **Final Result**:
Therefore, the decimal equivalent of the binary number \( (11101011)_2 \) is \( 235 \).

### Final Answer:
The resulting number in decimal is \( 235 \).

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