The binary representation of the decimal number 45 is

Options

A. 110011
B. 101010
C. 1101101
D. 101101

Explanation

To convert the decimal number 45 to its binary representation, we can use the method of successive division by 2. Here’s a step-by-step solution:

### Step 1: Divide the number by 2
- **Divide 45 by 2.**
- Quotient: 22
- Remainder: 1

### Step 2: Continue dividing the quotient by 2
- **Divide 22 by 2.**
- Quotient: 11
- Remainder: 0

### Step 3: Repeat the division
- **Divide 11 by 2.**
- Quotient: 5
- Remainder: 1

### Step 4: Continue the process
- **Divide 5 by 2.**
- Quotient: 2
- Remainder: 1

### Step 5: Keep dividing
- **Divide 2 by 2.**
- Quotient: 1
- Remainder: 0

### Step 6: Final division
- **Divide 1 by 2.**
- Quotient: 0
- Remainder: 1

### Step 7: Collect the remainders
Now, we collect all the remainders from the last division to the first:
- Remainders (from last to first): 1, 0, 1, 1, 0, 1

### Step 8: Write the binary representation
Thus, the binary representation of the decimal number 45 is:
- **Binary: 101101**

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

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