Decimal from 2s complement 11110010 – UGC NET Question

Since the leading bit is 1, 11110010₂ is negative in two's complement. Inverting the bits gives 00001101₂, and adding 1 yields 00001110₂, which is 14 in decimal. Therefore, the original pattern represents −14.

Option A:
Option A properly uses the inversion-plus-one procedure to decode the two's complement representation. It finds the magnitude as 14 and attaches the negative sign, giving −14.

Option B:
Option B, −12, would require the magnitude after inversion and increment to be 12, which does not match the computed 14.

Option C:
Option C, −10, similarly fails to align with the actual magnitude and indicates a miscalculation.

Option D:
Option D, −18, corresponds to a different two's complement pattern (11101110₂) and not to 11110010₂.