Step-by-step Solution:

To convert the decimal number 45 to binary, we use the method of successive division by 2: 1. 45 ÷ 2 = 22 remainder 1 2. 22 ÷ 2 = 11 remainder 0 3. 11 ÷ 2 = 5 remainder 1 4. 5 ÷ 2 = 2 remainder 1 5. 2 ÷ 2 = 1 remainder 0 6. 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top gives us the binary representation: 101101.