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\(_2\)