The binary representation of the decimal number 45 is:

Options

A. 110011
B. 101010
C. 110110
D. 101101

Answer

To convert the decimal number 45 into its binary representation, we can follow these steps:

### Step-by-Step Solution:

1. **Divide the Decimal Number by 2**:
Start by dividing the decimal number (45) by 2.
- 45 ÷ 2 = 22 with a remainder of 1.

2. **Record the Remainder**:
Write down the remainder (1). This will be the least significant bit (LSB) of the binary number.

3. **Continue Dividing the Quotient by 2**:
Take the quotient (22) and divide it by 2.
- 22 ÷ 2 = 11 with a remainder of 0.

4. **Record the Remainder**:
Write down the remainder (0).

5. **Repeat the Process**:
Continue this process:
- 11 ÷ 2 = 5 with a remainder of 1.
- 5 ÷ 2 = 2 with a remainder of 1.
- 2 ÷ 2 = 1 with a remainder of 0.
- 1 ÷ 2 = 0 with a remainder of 1.

6. **Collect All Remainders**:
Now, collect all the remainders from the last division to the first:
- From the last division to the first, we have: 1, 0, 1, 1, 1, 0, 1.

7. **Write the Binary Representation**:
Reading the remainders from bottom to top gives us the binary representation of 45:
- Therefore, the binary representation of 45 is **101101**.

### Final Answer:
The binary representation of the decimal number 45 is **101101**.

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