The number of 1’s in the binary representation of the value of 16^3 ×9+16^2…
2023
The number of 1’s in the binary representation of the value of
16^3 ×9+16^2 ×7+16×5+3
- A.
15
- B.
9
- C.
12
- D.
More than one of the above
- E.
None of the above
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Correct answer: B
The expression 16^3 × 9 + 16^2 × 7 + 16 × 5 + 3 evaluates to a decimal number. First, compute each term: 16^3 = 4096, so 4096 × 9 = 36864; 16^2 = 256, so 256 × 7 = 1792; 16 × 5 = 80; and the constant term is 3. Adding these gives 36864 + 1792 = 38656, plus 80 is 38736, and adding 3 gives 38739. Now convert 38739 to binary by repeatedly dividing by 2 and tracking remainders. The resulting binary representation has exactly 9 ones.