What is the binary representation of the decimal number 19?

To convert the decimal number 19 into its binary representation, you can use the process of repeatedly dividing the number by 2 and recording the remainders. When you do this for 19, the steps are as follows:

1. 19 divided by 2 gives a quotient of 9 and a remainder of 1.

2. 9 divided by 2 gives a quotient of 4 and a remainder of 1.

3. 4 divided by 2 gives a quotient of 2 and a remainder of 0.

4. 2 divided by 2 gives a quotient of 1 and a remainder of 0.

5. 1 divided by 2 gives a quotient of 0 and a remainder of 1.

Now, you take the remainders from the last division to the first division: 10011. Therefore, the binary representation of the decimal number 19 is indeed 10011.

This method systematically builds the binary representation, confirming that C is the correct answer.