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`

Answer

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

### Step-by-Step Solution:

**Step 1: Convert the integer part (13) to binary.**

1. Divide the integer by 2 and record the quotient and the remainder.
- 13 ÷ 2 = 6, remainder = 1
2. Divide the quotient by 2 again.
- 6 ÷ 2 = 3, remainder = 0
3. Divide the new quotient by 2.
- 3 ÷ 2 = 1, remainder = 1
4. Finally, divide the last quotient by 2.
- 1 ÷ 2 = 0, remainder = 1

Now, we write down the remainders in reverse order:
- From bottom to top: 1, 1, 0, 1

Thus, the binary equivalent of the integer part `13` is `1101`.

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

1. Multiply the fractional part by 2.
- 0.625 × 2 = 1.250 (Take the integer part, which is 1)
2. Take the fractional part (0.250) and multiply by 2 again.
- 0.250 × 2 = 0.500 (Take the integer part, which is 0)
3. Take the fractional part (0.500) and multiply by 2.
- 0.500 × 2 = 1.000 (Take the integer part, which is 1)

Since we reached a fractional part of 0.000, we can stop here. The binary digits obtained from the integer parts are:
- First digit: 1
- Second digit: 0
- Third digit: 1

Thus, the binary equivalent of the fractional part `0.625` is `101`.

**Step 3: Combine both parts.**

Now, we combine the binary representations of the integer part and the fractional part:
- Integer part: `1101`
- Fractional part: `101`

Putting them together, we get:
- The binary equivalent of `13.625` is `1101.101`.

### Final Answer:
The equivalent binary number of the decimal number `13.625` is **`1101.101`**.