Question

The number of 1's in the binary representation of $13 \times 16^3 + 11 \times 16^2 + 9 \times 16 + 3$?

• A. 9
• B. 8
• C. 10
• D. 12

Hint:

To convert a decimal number to binary, divide by 2 and record the remainders, then reverse the order of the remainders.

Answer 1

The Correct Option is C

First, calculate the expression \( 13 \times 16^3 + 11 \times 16^2 + 9 \times 16 + 3 \). This gives us: \[ 13 \times 16^3 + 11 \times 16^2 + 9 \times 16 + 3 = 13 \times 4096 + 11 \times 256 + 9 \times 16 + 3 = 53248 + 2816 + 144 + 3 = 56111 \] Now, convert \( 56111 \) to its binary representation: \[ 56111_{10} = 1101101011011111_2 \] There are 10 ones in the binary representation.
Thus, the number of 1's in the binary representation is \( 10 \).