The decimal equivalent of the binary number `(11010.101)_(2)` is

Options

A. 9.625
B. 25.265
C. 26.625
D. 26.265

Answer

To convert the binary number \( (11010.101)_2 \) into its decimal equivalent, we will follow these steps:

### Step 1: Identify the binary number
The binary number given is \( 11010.101 \).

### Step 2: Separate the integer and fractional parts
The integer part is \( 11010 \) and the fractional part is \( 101 \).

### Step 3: Convert the integer part to decimal
To convert the integer part \( 11010 \) to decimal, we will use the formula:
\[ \text{Decimal} = b_n \times 2^n + b_{n-1} \times 2^{n-1} + \ldots + b_1 \times 2^1 + b_0 \times 2^0 \]
Where \( b \) is the binary digit and \( n \) is the position from the right (starting from 0).

For \( 11010 \):
- \( 1 \times 2^4 = 1 \times 16 = 16 \)
- \( 1 \times 2^3 = 1 \times 8 = 8 \)
- \( 0 \times 2^2 = 0 \times 4 = 0 \)
- \( 1 \times 2^1 = 1 \times 2 = 2 \)
- \( 0 \times 2^0 = 0 \times 1 = 0 \)

Now, add these values:
\[ 16 + 8 + 0 + 2 + 0 = 26 \]

### Step 4: Convert the fractional part to decimal
To convert the fractional part \( 101 \) to decimal, we will use the formula:
\[ \text{Decimal} = b_{-1} \times 2^{-1} + b_{-2} \times 2^{-2} + b_{-3} \times 2^{-3} \]

For \( 101 \):
- \( 1 \times 2^{-1} = 1 \times 0.5 = 0.5 \)
- \( 0 \times 2^{-2} = 0 \times 0.25 = 0 \)
- \( 1 \times 2^{-3} = 1 \times 0.125 = 0.125 \)

Now, add these values:
\[ 0.5 + 0 + 0.125 = 0.625 \]

### Step 5: Combine the integer and fractional parts
Now, combine the results from the integer and fractional parts:
\[ 26 + 0.625 = 26.625 \]

### Final Answer
The decimal equivalent of the binary number \( (11010.101)_2 \) is \( 26.625 \).

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