Which of the following multiples an integer x8 by 10.25?Group of answer choices(x8 << 3) + (x8 << 2) + (x8 >> 1)(x8 << 3) + x8 + (x8 >> 2)(x8 >> 3) + (x8 >> 1) + (x8 << 2)(x8 << 3) + (x8 << 2) + (x8 >> 2)(x8 << 3) + (x8 << 1) + (x8 >> 2
Question
Which of the following multiples an integer x8 by 10.25?Group of answer choices(x8 << 3) + (x8 << 2) + (x8 >> 1)(x8 << 3) + x8 + (x8 >> 2)(x8 >> 3) + (x8 >> 1) + (x8 << 2)(x8 << 3) + (x8 << 2) + (x8 >> 2)(x8 << 3) + (x8 << 1) + (x8 >> 2
Solution
The correct answer is (x8 << 3) + (x8 << 1) + (x8 >> 2).
Here's why:
The << and >> are bitwise shift operators in programming. x << n means shifting the bits of x, n places to the left, which is equivalent to multiplying x by 2^n. Similarly, x >> n means shifting the bits of x, n places to the right, which is equivalent to dividing x by 2^n.
So, let's break down the expression (x8 << 3) + (x8 << 1) + (x8 >> 2):
- x8 << 3 is equivalent to x8 * 2^3 = x8 * 8
- x8 << 1 is equivalent to x8 * 2^1 = x8 * 2
- x8 >> 2 is equivalent to x8 / 2^2 = x8 / 4
Adding these together gives us x8 * 8 + x8 * 2 + x8 / 4 = 10x8 + 0.25x8 = 10.25x8, which is exactly what we want.
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