Range of 4 bit twos complement – UGC NET Question

In n-bit two's complement, the range is from -2^(n-1) to 2^(n-1) - 1. For 4 bits, this becomes -2^3 to 2^3 - 1. That gives a range from -8 to +7. Therefore, -8 to +7 is the correct range for 4-bit two's complement representation.

Option A:
Option A correctly states -8 to +7 as the range. This follows directly from the general two's complement range formula. It also matches the fact that 1000 represents -8 and 0111 represents +7 in 4-bit two's complement.

Option B:
Option B gives -7 to +8, which reverses the correct extremes. Two's complement always has one extra negative value, not one extra positive value. Therefore, this interval does not match the established formula for two's complement ranges.

Option C:
Option C claims -16 to +15, which is the range for a 5-bit two's complement system. It correctly follows the pattern for 5 bits, not 4 bits. Hence it does not apply to the specific case of 4-bit representation here.

Option D:
Option D states 0 to +15, which is the range for 4-bit unsigned binary. Two's complement is a signed representation and must include both negative and positive numbers. Therefore, a purely non-negative range cannot be correct for the given representation.