To convert the decimal number 39 to base 2, we can use the method of successive division by 2 and record the remainders. Here’s the process: 1. Divide 39 by 2: \(39 \div 2 = 19 \quad \text{remainder: } 1\) 2. Divide 19 by 2: \(19 \div 2 = 9 \quad \text{remainder: } 1\) 3. Divide 9 by 2: \(9 \div 2 = 4 \quad \text{remainder: } 1\) 4. Divide 4 by 2: \(4 \div 2 = 2 \quad \text{remainder: } 0\) 5. Divide 2 by 2: \(2 \div 2 = 1 \quad \text{remainder: } 0\) 6. Divide 1 by 2: \(1 \div 2 = 0 \quad \text{remainder: } 1\) Now, we read the remainders from bottom to top: Thus, the binary representation of 39 is: 100111\(_2\)