Bits Used for Storing Signed Integers

Signed integers are used to represent both positive and negative values in programming. The number of bits required to store signed integers depends on the maximum and minimum values that need to be represented.

- A signed integer can be represented using 1 bit for the sign and the remaining bits for the magnitude.
- The magnitude of a signed integer is the absolute value of the number without the sign bit.

For example, consider a signed integer with 8 bits. The sign bit is the most significant bit (leftmost bit) and the remaining 7 bits represent the magnitude.

- If the sign bit is 0, the number is positive and the magnitude is represented using the remaining 7 bits.
- If the sign bit is 1, the number is negative and the magnitude is represented using the 2's complement of the remaining 7 bits.

The maximum and minimum values that can be represented using n bits for signed integers are:

- Maximum value = 2^(n-1) - 1
- Minimum value = -2^(n-1)

For example, consider a signed integer with 16 bits. The maximum and minimum values that can be represented are:

- Maximum value = 2^(16-1) - 1 = 32767
- Minimum value = -2^(16-1) = -32768

Therefore, the number of bits required for storing signed integers depends on the range of values that need to be represented. In general, larger ranges require more bits. The correct answer for this question is option D, which represents 16 bits, since it can represent a wider range of values compared to the other options.