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`

Answer

To convert the decimal number 32.25 into its binary equivalent, we will break it down into two parts: the integer part (32) and the fractional part (0.25).

### Step-by-Step Solution:

1. **Convert the Integer Part (32) to Binary:**
- Divide the integer by 2 and record the quotient and the remainder.
- Continue dividing the quotient by 2 until the quotient becomes 0.

**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

Now, we collect the remainders from bottom to top:
- The binary representation of 32 is **100000**.

2. **Convert the Fractional Part (0.25) to Binary:**
- Multiply the fractional part by 2 and record the whole number part (0 or 1).
- Continue multiplying the fractional part by 2 until the fractional part becomes 0 or until you reach the desired precision.

**Calculations:**
- 0.25 × 2 = 0.5 → whole part = 0
- 0.5 × 2 = 1.0 → whole part = 1

The binary representation of 0.25 is **0.01** (we take the whole parts in the order they were obtained).

3. **Combine Both Parts:**
- Now, we combine the binary representation of the integer part and the fractional part.
- The integer part is **100000** and the fractional part is **0.01**.

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**.

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