Range of 8-bit 2s complement – UGC NET Question

For n-bit two's complement representation, the range is −2^(n−1) to 2^(n−1) − 1. With n = 8, this evaluates to −2⁷ to 2⁷ − 1, i.e., −128 to +127. One more negative value is representable than positive due to the asymmetry in the coding. Thus, the range of 8-bit two's complement integers is −128 to +127.

Option A:
Option A correctly applies the general formula for two's complement bounds. It recognises that 10000000₂ encodes −128 and 01111111₂ encodes +127, covering all 256 possible bit patterns.

Option B:
Option B, −127 to +127, omits the extra negative value and would imply a redundant representation or a symmetric sign-magnitude system. This does not match two's complement behavior.

Option C:
Option C, −128 to +128, includes 257 distinct integers, which exceeds the 256 patterns available in 8 bits. It therefore cannot be the valid range.

Option D:
Option D, −127 to +128, is both shifted and symmetric in a way that is inconsistent with two's complement encoding. It incorrectly adds a positive value that is not representable.