What is the binary number equivalent of the decimal number 32.25?

Options

A. `100010.10`
B. `100000.10`
C. `100010.01`
D. `100000.01`

Explanation

To convert the decimal number 32.25 into its binary equivalent, we will handle the integer and fractional parts separately.

### Step-by-Step Solution:

1. **Convert the Integer Part (32) to Binary:**
- Divide the integer by 2 and record the remainder.
- Continue dividing the quotient by 2 until you reach 0.
- Write down the remainders in reverse order.

**Calculations:**
- 32 ÷ 2 = 16, remainder = 0
- 16 ÷ 2 = 8, remainder = 0
- 8 ÷ 2 = 4, remainder = 0
- 4 ÷ 2 = 2, remainder = 0
- 2 ÷ 2 = 1, remainder = 0
- 1 ÷ 2 = 0, remainder = 1

**Binary Representation of 32:**
- Reading the remainders from bottom to top, we get: 100000.

2. **Convert the Fractional Part (0.25) to Binary:**
- Multiply the fractional part by 2.
- The whole number part of the result will be the next binary digit.
- Continue with the new fractional part until it becomes 0 or until you reach the desired precision.

**Calculations:**
- 0.25 × 2 = 0.50 → whole number part = 0
- 0.50 × 2 = 1.00 → whole number part = 1

**Binary Representation of 0.25:**
- The binary representation is 01.

3. **Combine Both Parts:**
- Combine the binary representations of the integer and fractional parts.
- The integer part (32) is 100000 and the fractional part (0.25) is 01.

**Final Binary Representation:**
- Therefore, the binary equivalent of the decimal number 32.25 is: **100000.01**.

### Final Answer:
The binary number equivalent of the decimal number 32.25 is **100000.01**.