What is the binary equivalent of the decimal number 0.3125?

Options

A. 0.0111
B. 0.101
C. 0.0101
D. 0.1101

Explanation

To convert the decimal number 0.3125 into its binary equivalent, we can follow these steps:

### Step-by-Step Solution:

1. **Multiply by 2**: Start by multiplying the decimal number (0.3125) by 2.
\[ 0.3125 \times 2 = 0.625 \]
**Hint**: When converting a decimal fraction to binary, multiplying by 2 helps to shift the decimal point to the right.

2. **Extract the Integer Part**: The integer part of the result (0.625) is 0. Write this down.
- Current binary result: 0

3. **Repeat the Process**: Now take the fractional part (0.625) and multiply it by 2.
\[ 0.625 \times 2 = 1.25 \]
**Hint**: Always focus on the fractional part after each multiplication.

4. **Extract the Integer Part**: The integer part of the result (1.25) is 1. Write this down.
- Current binary result: 0.1

5. **Continue Multiplying**: Take the fractional part (0.25) and multiply it by 2.
\[ 0.25 \times 2 = 0.5 \]
**Hint**: Keep multiplying the fractional part until it becomes 0 or you reach a desired precision.

6. **Extract the Integer Part**: The integer part of the result (0.5) is 0. Write this down.
- Current binary result: 0.10

7. **Repeat Again**: Now take the fractional part (0.5) and multiply it by 2.
\[ 0.5 \times 2 = 1.0 \]
**Hint**: Each time you multiply, note the integer part and continue with the fractional part.

8. **Extract the Integer Part**: The integer part of the result (1.0) is 1. Write this down.
- Current binary result: 0.100

9. **Final Result**: Since the last multiplication resulted in 0, we can stop here. The binary equivalent of the decimal number 0.3125 is:
\[ 0.1001 \]

### Final Answer:
The binary equivalent of the decimal number 0.3125 is **0.1001**.