if x is an int, is the following statement always true? x & 5= = 5 implies (x<<29) <0 True False

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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### Question:

If \( x \) is an int, is the following statement always true?

\[ x \& 5 == 5 \text{ implies } (x \ll 29) < 0 \]

- ○ True
- ○ False

### Explanation:

This question involves bitwise operations and comparisons. It requires understanding the behavior of bitwise AND (`&`) and left shift (`<<`) operators in binary operations on integers. When analyzing the expression:

- **`x & 5 == 5`**: This checks if the bitwise AND of `x` and `5` results in `5`. This means that the last two bits of `x` must be `101` (since 5 is `101` in binary).

- **`(x << 29) < 0`**: This expression left shifts `x` by 29 bits, and then checks if the result is less than zero. For the output to be negative, the leftmost bit (which is the sign bit in a 32-bit signed integer) must be `1`.

Understanding these operators and their effects on integers is crucial for correctly evaluating whether the statement is true or false.
Transcribed Image Text:### Question: If \( x \) is an int, is the following statement always true? \[ x \& 5 == 5 \text{ implies } (x \ll 29) < 0 \] - ○ True - ○ False ### Explanation: This question involves bitwise operations and comparisons. It requires understanding the behavior of bitwise AND (`&`) and left shift (`<<`) operators in binary operations on integers. When analyzing the expression: - **`x & 5 == 5`**: This checks if the bitwise AND of `x` and `5` results in `5`. This means that the last two bits of `x` must be `101` (since 5 is `101` in binary). - **`(x << 29) < 0`**: This expression left shifts `x` by 29 bits, and then checks if the result is less than zero. For the output to be negative, the leftmost bit (which is the sign bit in a 32-bit signed integer) must be `1`. Understanding these operators and their effects on integers is crucial for correctly evaluating whether the statement is true or false.
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