What is the binary equivalent of decimal number `(0.8125)_(10)`?

Options

A. `(0.1101)_(2)`
B. `(0.1001)_(2)`
C. `(0.1111)_(2)`
D. `(0.1011)_(2)`

Explanation

To convert the decimal number \( (0.8125)_{10} \) to its binary equivalent, we will follow these steps:

### Step 1: Multiply by 2
Start with the decimal number \( 0.8125 \) and multiply it by \( 2 \).

\[ 0.8125 \times 2 = 1.625 \]

### Step 2: Record the Integer Part
The integer part of the result is \( 1 \). This will be the first digit after the binary point.

### Step 3: Take the Fractional Part
Now take the fractional part \( 0.625 \) and multiply it by \( 2 \).

\[ 0.625 \times 2 = 1.25 \]

### Step 4: Record the Integer Part
The integer part of this result is \( 1 \). This will be the second digit after the binary point.

### Step 5: Continue with the Fractional Part
Next, take the fractional part \( 0.25 \) and multiply it by \( 2 \).

\[ 0.25 \times 2 = 0.5 \]

### Step 6: Record the Integer Part
The integer part here is \( 0 \). This will be the third digit after the binary point.

### Step 7: Continue with the Fractional Part
Now take the fractional part \( 0.5 \) and multiply it by \( 2 \).

\[ 0.5 \times 2 = 1.0 \]

### Step 8: Record the Integer Part
The integer part is \( 1 \). This will be the fourth digit after the binary point.

### Step 9: Combine the Results
Now, we combine all the integer parts we recorded in order:

- From Step 2: \( 1 \)
- From Step 4: \( 1 \)
- From Step 6: \( 0 \)
- From Step 8: \( 1 \)

Thus, the binary equivalent of \( (0.8125)_{10} \) is:

\[ (0.1101)_2 \]

### Final Answer
The binary equivalent of the decimal number \( (0.8125)_{10} \) is \( (0.1101)_2 \).

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