Question

The binary representation of 60 is

• A. 101110
• B. 111100
• C. 110011
• D. 110000

Hint:

Read remainders from bottom to top.

Answer 1

The Correct Option is B

To find the binary representation of the decimal number 60, we need to convert it from decimal to binary. Let's explain the step-by-step process of this conversion:

1. Divide the Decimal Number by 2:
   • 60 ÷ 2 = 30 (remainder 0)
   • 30 ÷ 2 = 15 (remainder 0)
   • 15 ÷ 2 = 7 (remainder 1)
   • 7 ÷ 2 = 3 (remainder 1)
   • 3 ÷ 2 = 1 (remainder 1)
   • 1 ÷ 2 = 0 (remainder 1)
2. Write down the remainders in reverse order:
   • The remainders from last to first are: 111100

Thus, the binary representation of the decimal number 60 is 111100. This matches the given option: 111100.

Now, let's briefly verify why the other options do not represent the binary of 60:

• 101110: In decimal, this is equivalent to 46.
• 110011: In decimal, this is equivalent to 51.
• 110000: In decimal, this is equivalent to 48.

Therefore, the correct binary representation of the number 60 is indeed 111100.