Convert decimal 99 to binary.

• A. 1100101
• B. 1101001
• C. 11100011
• D. 1100011

To convert the decimal number 99 into binary, we can use a method called repeated division by 2. This process involves dividing the number by 2 and keeping track of the remainders. The binary representation is then formed by reading these remainders in reverse order. Let’s break it down step by step.

Step-by-Step Conversion

1. **Divide the number by 2**: Start with 99 and divide it by 2. Write down the quotient and the remainder.

2. **Record the remainder**: The remainder will be either 0 or 1, which is the essence of binary digits.

3. **Repeat the process**: Continue dividing the quotient by 2 until the quotient becomes 0.

Performing the Division

• 99 ÷ 2 = 49, remainder = 1
• 49 ÷ 2 = 24, remainder = 1
• 24 ÷ 2 = 12, remainder = 0
• 12 ÷ 2 = 6, remainder = 0
• 6 ÷ 2 = 3, remainder = 0
• 3 ÷ 2 = 1, remainder = 1
• 1 ÷ 2 = 0, remainder = 1

Compiling the Binary Number

Now, let’s gather the remainders from the last division to the first:

• 1 (from 1 ÷ 2)
• 1 (from 3 ÷ 2)
• 0 (from 6 ÷ 2)
• 0 (from 12 ÷ 2)
• 0 (from 24 ÷ 2)
• 1 (from 49 ÷ 2)
• 1 (from 99 ÷ 2)

Reading these remainders from bottom to top gives us: 1100011.

Final Result

The binary representation of the decimal number 99 is 1100011. Therefore, the correct answer from the options provided is:

D. 1100011

This method of conversion is quite useful and can be applied to any decimal number to find its binary equivalent. Understanding this process not only helps in binary conversion but also strengthens your grasp of number systems in general.