What is the binary representation of the decimal number 19?

What is the binary representation of the decimal number 19?

• A. 10010
• B. 11001
• C. 10011
• D. 11111

Answer: (C)

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.

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.