What is the equivalent binary number of the decimal number 13.625?

Options

A. `1101.111`
B. `1111.101`
C. `1101.101`
D. `1111.111`

Explanation

To convert the decimal number 13.625 into its equivalent binary number, we can break the process into two parts: converting the whole number part (13) and the fractional part (0.625) separately.

### Step 1: Convert the whole number part (13) to binary

1. **Divide the number by 2** and keep track of the quotient and remainder.
- 13 ÷ 2 = 6, remainder = 1
- 6 ÷ 2 = 3, remainder = 0
- 3 ÷ 2 = 1, remainder = 1
- 1 ÷ 2 = 0, remainder = 1

2. **Write down the remainders in reverse order**:
- Reading the remainders from bottom to top gives us: 1101

Thus, the binary representation of the whole number 13 is **1101**.

### Step 2: Convert the fractional part (0.625) to binary

1. **Multiply the fractional part by 2** and take note of the integer part:
- 0.625 × 2 = 1.25 → integer part = 1
- 0.25 × 2 = 0.5 → integer part = 0
- 0.5 × 2 = 1.0 → integer part = 1

2. **Write down the integer parts**:
- The integer parts from the multiplications are: 1, 0, 1

Thus, the binary representation of the fractional part 0.625 is **101**.

### Final Step: Combine both parts

Combining the whole number part and the fractional part, we get:
- Whole number part: 1101
- Fractional part: 101

Therefore, the equivalent binary number of the decimal number 13.625 is **1101.101**.

### Summary
The equivalent binary number of the decimal number 13.625 is **1101.101**.

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