Decimal of binary 0.1011 – UGC NET Question

The bits after the binary point correspond to 1/2, 1/4, 1/8, and 1/16. In 0.1011₂, we have 1×1/2 + 0×1/4 + 1×1/8 + 1×1/16 = 0.5 + 0 + 0.125 + 0.0625 = 0.6875. Thus, the decimal value of 0.1011₂ is 0.6875.

Option A:
Option A correctly sums the contributions of the 2⁻¹, 2⁻³, and 2⁻⁴ places and omits the 2⁻² place because its bit is zero. The resulting 0.6875 accurately reflects the binary pattern.

Option B:
Option B, 0.625, equals 0.5 + 0.125 and would correspond to 0.101₂, which has only three fractional bits. It neglects the contribution of the 2⁻⁴ bit.

Option C:
Option C, 0.75, corresponds to 0.11₂ (0.5 + 0.25) and does not match the given bit arrangement.

Option D:
Option D, 0.5625, equals 0.5 + 0.0625, which would correspond to 0.1001₂. This ignores the 2⁻³ bit present in 0.1011₂.