What is the binary value of an 8-bit counter after counting one hundred balls?

To determine the binary value of an 8-bit counter after counting one hundred balls, we first need to convert the decimal number 100 into its binary equivalent.

Starting with the binary conversion process, we can break down 100 by repeatedly dividing by 2 and noting the remainders:

1. 100 ÷ 2 = 50 with a remainder of 0

2. 50 ÷ 2 = 25 with a remainder of 0

3. 25 ÷ 2 = 12 with a remainder of 1

4. 12 ÷ 2 = 6 with a remainder of 0

5. 6 ÷ 2 = 3 with a remainder of 0

6. 3 ÷ 2 = 1 with a remainder of 1

7. 1 ÷ 2 = 0 with a remainder of 1

Now we can read the binary digits from bottom to top, which gives us 1100100. However, since we need an 8-bit representation, we add an extra leading zero to ensure it fits within 8 bits. Therefore, the complete binary representation of 100 in an 8-bit format is `01100100