UGC NET Questions (Paper – 1)

In an n-bit two's complement system, the value of a bit pattern is given by -2ⁿ⁻¹ for the sign bit plus the sum of remaining positive powers where bits are set. When all bits are 1, the negative sign bit contributes -2ⁿ⁻¹ and all other bits sum to 2ⁿ⁻¹ - 1. Adding these gives -2ⁿ⁻¹ + (2ⁿ⁻¹ - 1) = -1. Thus, the all-ones pattern always represents -1. Hence, option A is correct.

Option A:
Option A correctly reflects this cancellation property. The all-ones pattern has a fixed meaning of -1 in two's complement for any bit-width.

Option B:
Option B, 0, is represented by all bits 0, not all ones. So it does not match the pattern.

Option C:
Option C, the largest positive integer, is 011…1 (sign bit 0, rest 1s), not 111…1.

Option D:
Option D is incorrect because all bit patterns are defined in two's complement; 111…1 is a valid integer equal to -1.