Decimal value of 1’s complement – UGC NET Question

In 8-bit one’s complement, a leading 1 indicates a negative number. To find its magnitude, invert all bits and read the result as an unsigned binary number. Inverting 10011001₂ gives 01100110₂, which equals 64 + 32 + 4 + 2 = 102. Therefore, 10011001₂ represents −102 in one’s complement.

Option A:
Option A is correct because one’s complement encodes −X as the bitwise inversion of +X. Since 10011001₂ inverts to 01100110₂ (= 102), the represented value is −102.

Option B:
Option B (−104) would require the inverted magnitude to be 104 (01101000₂). But the inversion here is 01100110₂ (=102), so it cannot be −104.

Option C:
Option C (−127) is the most negative magnitude possible in 8-bit one’s complement and corresponds to inverting 01111111₂. The given pattern does not invert to 127, so this is incorrect.

Option D:
Option D (−128) is not representable in 8-bit one’s complement (the range is −127 to +127, with both +0 and −0). Hence −128 cannot be the answer.