Which range of values is valid for all integral types, where n is the number of bits?

  1. 2^(n-1) to 2^(n+1)+1

  2. -2^(n-1) to 2^(n-1)-1

  3. -2^(n-1) to 2^(n-1)+1

  4. -2^(n-1) to 2^(n+1)-1


Correct Option: B

AI Explanation

To answer this question, you need to understand the range of values that can be represented by integral types.

Integral types include signed and unsigned integers. The range of values for signed integers depends on the number of bits used to represent them.

For a signed integer with n bits, the range of values that can be represented is from -2^(n-1) to 2^(n-1)-1. This means that the most significant bit is used to represent the sign of the number (0 for positive, 1 for negative), and the remaining n-1 bits are used to represent the magnitude of the number.

Let's go through each option to understand why it is correct or incorrect:

Option A) 2^(n-1) to 2^(n+1)+1 - This option is incorrect because it includes values outside the valid range for signed integers.

Option B) -2^(n-1) to 2^(n-1)-1 - This option is correct. It represents the valid range for signed integers, where the most significant bit represents the sign bit.

Option C) -2^(n-1) to 2^(n-1)+1 - This option is incorrect because it includes an extra value (2^(n-1)+1) outside the valid range for signed integers.

Option D) -2^(n-1) to 2^(n+1)-1 - This option is incorrect because it includes values outside the valid range for signed integers.

Therefore, the correct answer is B. The range of values that is valid for all integral types, where n is the number of bits, is -2^(n-1) to 2^(n-1)-1.

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