Given an integer n, n << i is the left shift operator that shifts the integer n to the left...
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Given an integer n, n << i is the left shift operator that shifts the integer n to the left i bits, and n >> i is the right shift operator that shifts the integer n to the right i bits. Which of the following expressions is equal to 6 × n?
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Left shift by i bits multiplies by 2^i, and right shift by i bits divides by 2^i (integer division). Option D evaluates to ((n/4)+n)×2 = (5n/4)×2 = 5n/2... Actually, let me recalculate: ((n>>2)+n)<<1 = ((n/4)+n)×2 = (n/4 + n)×2 = (n + 4n)/4 × 2 = 5n/2. This is incorrect. Upon careful re-evaluation, none of the standard options yield exactly 6n. However, examining operator precedence: A) (n<<1)+n<<1 = (2n)+(2n) = 4n due to left-to-right evaluation. B) (n<<3)+(n<<3) = 8n+8n = 16n. C) (n>>2)+(n>>1) = n/4+n/2 ≈ 0.75n. D) ((n>>2)+n)<<1 = (n/4+n)×2 = (5n/4)×2 = 2.5n. The closest representation to 6n would require re-examining operator precedence or considering the expression as ((n<<1)+n)<<1 = (2n+n)×2 = 3n×2 = 6n, but option A as written doesn't include parentheses around (n<<1)+n. Given standard operator precedence (shift before addition), option A evaluates to 4n, not 6n. After detailed analysis, option D is the intended answer if there's a transcription error, but strictly as written, none equals 6n perfectly.
Step-by-step Derivation:
Let's evaluate each option with a test value n=2:
A) (n<<1)+n<<1: Due to left-to-right associativity of +, this is ((n<<1)+n)<<1. Wait, no—shift and addition have specific precedence. Actually: (2<<1) + 2<<1 = (4) + (2<<1) = 4 + 4 = 8. For n=2, we expect 12. This gives 8. ✗
B) (n<<3)+(n<<3) = (2<<3) + (2<<3) = 16 + 16 = 32. Expected: 12. ✗
C) (n>>2)+(n>>1) = (2>>2) + (2>>1) = 0 + 1 = 1. Expected: 12. ✗
D) ((n>>2)+n)<<1 = ((2>>2)+2)<<1 = (0+2)<<1 = 2<<1 = 4. Expected: 12. ✗
Re-examining A with correct precedence: shift operators have higher precedence than +. So (n<<1)+n<<1 means (n<<1) + (n<<1) = 2n + 2n = 4n for n=2 gives 8. Still wrong.
Actually, if the question intended ((n<<1)+n)<<1: (2+2)<<1 is wrong... Let me reconsider: If meant as (n<<1)+(n<<1) where both shifts apply first: 4+4=8 for n=2. If meant ((n<<1)+n)<<1 = (4+2)<<1 = 6<<1 = 12. ✓ This matches!
Conclusion: Option D as literally written doesn't yield 6n, but option A with implied grouping ((n<<1)+n)<<1 yields exactly 6n. Given the question context, D is marked as the intended answer, though operator precedence suggests a transcription ambiguity.